Wa'alaikumsalaam wa rahmatullah

The general rule is that no one will be punished for another person's deeds. 

"That no bearer of burdens will bear the burden of another." (53:38)

If a pious child prays for his/her parents, it is part of the continuous deeds based on this hadith:

The Messenger of Allah, ﷺ, said, “When the human being dies, his deeds end except for three: ongoing charity, beneficial knowledge, or a righteous child who prays for him.” (Muslim)

But on the other hand, if the reason for the child is not praying for his/her parents is because he/she did not receive sufficient religious education from their parents, it may bring difficulties to the parents in the grave and the hereafter.

Allah knows best

Wa'alaikumsalaam wa rahmatullah

A well known principle: all good deeds that remove sins only remove minor sins. Scholars have different opinions about this, but ultimately, Allah has a full authority to make exceptions for everything. Imam Nawawi rahimahullah said (paraphrased): "The sins in the hadith refer to the minor sins. If it's not just for minor sins, then it is hoped that Allah will make it easy for them to be forgiven for the major sins." 

Additionally, you can combine 3 intentions for this fast: 

1. Day of Arafah

2. Thursday

3. Making up for Ramadan

Allah knows best

1. The vast majority of scholars hold it to be permissible. It will be permissible In Shā Allāh. You don't need to only specify it for the deceased person alone, rather, you should do it on behalf of yourself as well as those who are deceased. The Prophet ﷺ would say: (In the name of Allah), O Allah, accept it from Muhammad, Muhammad's family and from Muhammad's Ummah." (Muslim). Doing it solely for the deceased is something scholars have differing opinions about.
2. Scholars have different opinions about the ruling of making udhiyah. The scholars who say it's fard are basing it on this hadith: The Messenger ﷺ said: "Whoever can afford to offer a sacrifice but does not do so, let him not approach our place of prayer."  (Ibnu Majah). But majority of the scholars say it's sunnah mu'akkadah (highly recommended) based on a hadith: "Whoever among you wants to offer a sacrifice, let him not take (cut) anything from his hair or nails." (al Bukhari) - This opinion is the stronger than the first one. Allah knows best. 
3. The udhiyah sacrifice suffices a person and their household, and based on the view that a person can include their deceased family members, the child can be included. Abu Ayyoob al-Ansaari (may Allah be pleased with him) said: “At the time of the Prophet ﷺ, a man would sacrifice a sheep on behalf of himself and his household, and they would eat some and give some to others.” (Ibnu Majah). Note: If a man sacrifices a single sheep or goat on behalf of himself and his family, that will suffice for everyone he intended of his family, whether living or deceased.  Note: One-seventh of a camel or cow is equivalent to one sheep; if a man sacrifices one-seventh of a camel or cow on behalf of himself and his family, that is sufficient.

Allah knows best.

wa'alaikumsalaam wa rahmatullah

1. Qiyam ul Layl surah recitations are done out loud (jahr) if you do it in a congregation. Otherwise, when you pray by yourself, you can recite the surah silently or out loud. The ruling of Qiyam ul layl is recommended (mustahab/sunnah)
2. If there is a najis (which there most likely is), the wudu is not valid. But if the person forgets and realizes it after making the salah, he/she doesn't have to repeat the salah. Please note, that water IS NOT a requirement to clean the najis. So a person can use tissue to wipe his private part after using the bathroom. The act of cleaning after using the bathroom is called istijmaar.

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Istijmaar or wiping oneself means removing impurity on both passages, front and back, with a stone or a tissue and the like. What is required in istijmaar is that the number of wipes should be no less than three, and to achieve purity, which is the removal of the impurity and making the place dry. The sign that purity has been attained is that the last wipe should come back dry with no trace of impurity on it. And if that is done, then the purpose has been fulfilled and the place has become pure.

Allah knows best

So here are some issues which your question is based on: 

Firstly, for a child who is not Mumayyiz (at the age of distinction, being able to understand speech and commands), their salah is not valid by Ijmaa' (scholarly consensus, no difference of opinion) 

A Mumayyiz according to many scholars is one who reaches the age of 7.  That being said, a 6 yr old's salah won't be valid. 

To clarify:

0-7: salah doesn't count. 

7-puberty: salah counts, but not an obligation. 

Puberty: salah is an obligation.

The proof of this is that the Prophet ﷺ said to command children to pray at the age of 7. Of course the parent will get the reward of encouragement.

Secondly, based on #1, he shouldn't be leading the salah, rather he'd pray next to the parent

Some scholars do say that a Mumayyiz can be younger than 7 if they are matured, remain focused in salah, understand instruction, etc.

So the general rule is that any loan which includes interest will fall under Ribaa. 

"The Messenger of Allah, ﷺ, cursed the one who consumes riba and the one who pays it, the one who writes it down and the two who witness it, and he said: they are all the same." (Muslim)

However, if you already are in debt, make tawbah, and pay it off as soon as possible.

Scholars say that using a credit card is problematic due to the riba contract in the beginning,  so we should not underestimate it. They say you can only use it in the time of necessity.

Wa'Alaykumus-Salāmu Wa Rahmatullāhi Wa Barakātuh.

Absolutely. It's best to have a madhhab as your base, and then if another opinion comes to you and you're genuinely convinced, then follow that. For example, if you follow the Hanbali madhhab like I do, and a view from Imam ash-Shafi'ee come and you agree with his view instead of Imam Ahmad's view, then there's nothing wrong with that. Rather that's what we should do.

There are three opinions on this issue:

1. Some say you shouldn't follow a madhhab at all! Follow the authentic hadith. However, the hadiths are not understood by me and you who have little knowledge. We must look at how the scholars of our tradition understood these texts. 

2. Others say you must stick to one madhhab and it is never permissible for you to go outside of the madhhab. 

This is as if they are making these madhhabs the statements of Allah and his messenger ﷺ. Only Allah and his Messengers are given this status. 

3. The middle ground that I mentioned in the beginning.

For this question, wearing the niqaab and avoiding plucking the eyebrows is not something exclusive to a particular madhab. It's something that a lot of other groups do as well. Simply explain to them that you're not part of any group, and you're just trying to follow the sunnah of the Prophet ﷺ. There are scholars of all 4 madhhabs who mandate the niqaab. There are also scholars of the past who allowed trimming the eyebrows like some of the Hanbali scholars, and there are those who forbade it completely, like the Maliki and Shafiee scholars.

In terms of avoiding Muslims, as long as someone isn't abandoning someone they already have a relationship with, then it's not a problem if the issue is about simply avoiding them.

Keep making du'a for them and if you can, keep treating them kindly and justly.

The Messenger ﷺ said:  “Islam began as something strange and will revert to being strange as it began, so give glad tidings to the strangers.” (narrated by Imam Muslim)

Allah knows best

Just because someone has feelings associated with the LGBT community doesn't mean that their Islam won't be valid. As long as they don't make it halal or justify it. May Allah guide them!

This is an issue of contention between the scholars of Tafseer. When examining the classical works of Tafseer, we find that there are 2 main views. They either say it was Ishaaq or Ismaa'eel. Some scholars also choose to remain silent as to who it actually was. 

The First View

The first view is that it was Ishaaq, and this was held by the majority of the scholars of tafseer. This may be surprising to many, but it is a fact that shows that this isn't the view of a fringe group. This view was held by many of the companions of the Prophet ﷺ. Al-Qurtubi attributes this view to al-Abbas, Ibn Abbas, Umar ibn al-Khattab, Abdullah ibn Umar, Jabir, Abdullah ibn Mas'ood, Ali ibn Abee Talib (Tafseer al-Qurtubi). Al-Qurtubi also attributes this view to a few of the Tabi'een as well. He attributes this view to ash-Sha'bi, Alqamah, Mujaahid, Sa'eed ibn Jubair, Ka'b al-Ahbaar, Masrooq, Qataadah, Ataa', Muqaatil, az-Zuhri, and others (Tafseer al-Qurtubi). He also attributes this view to Imam Maalik, as well as the People of the Book (Tafseer al-Qurtubi). This was also the view of Imam Ahmad in one narration (quoted by Ibn Taymiyyah in Majmoo' Fatawa). This was also the view of Ibn Jareer at-Tabari in his Tafseer, as well as Abu Ja'far an-Nuhaas in his Tafseer. 

The Second View

The second view is that it was Ismaa'eel, and this was held by a few scholars. This view was attributed to some of the companions. al-Qurtubi attributes this view to Abu Hurairah, Abu Tufail. (Tafseer al-Qurtubi). He also mentions that this view was also attributed to Ibn Abbas and Ibn Umar (the first view was attributed to them as well). This was also the view of Tabi'een such as ash-Sha'bi, Sa'eed ibn al-Musayyab, Mujahid, al-Kalbi, and Alqamah. This was also the view of Imam Ahmad in one narration (quoted by Ibn Taymiyyah in Majmoo' Fatawa). This was also the view of Ibn Taymiyyah in his Majmoo'Fatawa, Ibn Katheer in his Tafseer, as-Sa'di in his Tafseer, and others. Ibn Katheer also attributes this view to the People of the Book, and mentions that it is incorrect to attribute the view that it was Ishaaq to them (Tafseer ibn Katheer). He argues that there are verses in the Bible which clearly illustrate that it was Ismaa'eel who Ibraheem was commanded to sacrifice, not Ishaaq (Tafseer ibn Katheer).

Evidences of the First View

The scholars who held the first view site as evidence that Ibraheem was only given the glad tidings of one son in the Qur'an, and that was Ishaaq. "So We gave him good tidings of a forbearing boy." (37:101). This must be Ishaaq, because Ibraheem was only given the glad tidings of one son in the Quran, namely Ishaaq. (This argument was mentioned by al-Qurtubi in his Tafseer). The second point of evidence is that this was the view of the People of the Book, and the Prophet ﷺ allowed the companions to narrate from the People of the Book. There is also hadiths narrated to support this, but Ibn Katheer establishes that there is nothing authentic to support this. (Tafseer ibn Katheer) ash-Shawkaani mentions in his Tafseer that everything narrated from the Prophet ﷺ concerning this issue is either severely weak or fabricated. (Fath al-Qadeer). 

Evidences of the Second View

The scholars who held the second view cite the Quranic context as evidence. Verse (37:101) mentions a "forbearing boy", and then later, in verse (37:112), Allah says, "And We gave him good tidings of Ishaaq, a prophet from among the righteous." These scholars say that if verse 101 refers to Ishaaq, then why does Allah repeat himself in verse 112? There is a famous principle that "The general rule is that when speech continues, it is to establish new ideas, not to reinforce aforementioned ideas." (This was mentioned by Ibn Uthaymeen in his explanation of hadith#2 from an-Nawawi's 40 Hadith). The second main point these scholars bring up is that the claim that this is the view of the People of the Book is problematic, because from their own sources, it's contradictory to say that Ishaaq was meant to be sacrificed. After Ibn Katheer mentions this argument and establishes that what the People of the Book say isn't an evidence, he says that this was a forgery by the People of the Book to support their Israelite Prophet, Ishaaq. They did this to show that the Israelite Prophet Ishaaq is superior to the Prophet of the Arabs, Ismaa'eel (Tafseer ibn Katheer), This is a good example of the Prophetic statement, "not believe the people of the Book, nor disbelieve them." (Al-Bukhari). Thirdly, some of these scholars use Prophetic hadiths to support this claim, all of which are weak. Ash-Shawkaani mentions in his Tafseer that everything narrated from the Prophet ﷺ, concerning this issue (in term of the validity of the hadith) is either severely weak or fabricated. (Fath al-Qadeer). 

Conclusion

This is an issue with strong arguments on both sides. Personally, I think the second view is the strongest, and makes more sense. This is due to their evidences. There are some scholars such as ash-Shawkaani, who choose to remain silent. He mentions in his Tafseer that the evidences of both sides are strong, and no view seems to be stronger than the other. He says it's best and safer to remain silent on the issue. (Fath Al-Qadeer) 

Allah knows best.

Slavery is a long issue. 

Here are some points to consider: 

• Slavery has existed in one form or another in every society as far as we can trace human history in the past. 
• Slavery exists today in many different forms. (prison systems in the west, debt slaves, illegal immigrants being taken advantage of, human trafficking etc . . )
• The slavery of the Prophet ﷺ, and the companions cannot be compared to Western slavery.  The Prophet ﷺ said: “I eat just as the slave eats, and I sit just as the slave sits”. Abu Ya’la (Sahih). How many people sit down with their slaves or even servants when eating? Also he and his companions educated their slaves well, therefore some of them became leaders of the communities later on.
• There is no religion, or system of living which encourages the freeing of slaves more than Islam.  “He will be doubly rewarded,…the man who had a slave girl, and he fed her well, taught her manners and educated her, and then freed her and married her” [Al-Bukhari and Muslim.]
• There is no religion, or system of living which encourages the good treatment of slaves more than Islam.