I've been trying to avoid any bughz, keena , jealousy or feeling of inferiority to stay in peace and make my heart clear and pious and busy in the remembrance of Allah almighty but I'm not able to eradicate it from my heart.
Please tell me a way to clean my heart from every negative emotion for others and to keep it in peace. Tell me how can I maintain my self esteem and kindly do tell how to control the inappropriate Nafsani wills.

What you describe is the challenge of every believer, this is because there is a God-instilled innate drive for improvement. Unfortunately, love of worldly possession makes us covetous and it lowers our pursuit of higher things like spirituality. Thus, try to minimize the value of your own worldly possessions, especially by not giving them importance when you see them with others. Ponder on the lives of the m’asoomeen and remind yourself that true success will be in the next world. Finally, increase your recitation of the Holy Quran and supplicate and remember Allah constantly. May He give you guidance and success

I heard from someone that the early Shias were taught hadith science by the Sunnis. Is this true? And if not where did this come from

There is some contention and historic evidence that the Ahl al-Sunnah began examining the Hadith before the Shia, obviously this only could have happened after recourse to it was reinstituted by the ruling regime. On the other hand, the Shia could rely on the Imams (p) directly, at least until the time of the 10th, 11th and 12th Imams. Thus, although the basic science follows a similar process, there are differences (from my understanding), and this comes from independent implementation of its usage. I hope this helps, there are resources to read if you need further details.

Can I only pray salatul layl once a night?

It is a nafilah prayer so you can pray it as much or as little as you like. If you repeat it in the same night, then one option would be to do it’s qadha for past nights or gift it to a deceased relative And, remember certain scholars in your duas at that sacred time.

1) I've had a question on nawafil of dhuhr and asr. What is the time frame wherein we can pray those?

2) I saw somewhere that there's a very short time frame though, with a method of measurement involving a stick of sorts. Is that for other madhahib or does it apply to us as well?

3) At what length are you unallowed to pray the nawafil?

1) The time for each is before the respective obligatory salat.

2) The time for establishing dhuhr and asr can be achieved by looking at the shadow of a stick that is vertically placed in the ground. As the shadow gets longer the time is indicated to be progressing. Indeed the time for those nawafil is short when considering the actual start of the obligatory prayer period. But one can pray them nonetheless and then commence with the obligatory prayer.

3) You are never not allowed to pray nafilah, you can even pray it’s qadha. The only exception is if you have not prayed an obligatory prayer and it’s time is running out

Is white wine vinegar permissible

If it is certain that the white wine completely converted to vinegar then it is pure and permissible to consume

I recently got to know one of my university friends is qadiani. We have an interaction on daily basis, I try my best to avoid eating with her as much as possibly I can but sometimes we have to share our edibles even if i don't want to. Secondly, I wanted to ask that whenever we buy something sometimes she pays the bill. Someone told me that as they are not the believers of our last prophet so they are not muslims, hence they are najis. So, you cannot eat with them in a single plate or the crockery they have used should also be purified. Is it?

There is no problem in eating with them or having them pay for your food as long as there is nothing haram.

I have not read that they are kafir and najis. Qadianis are not considered to be Muslim but the question of whether they are najis is not known. If you are worried then you can practice precaution

1) I've been wanting to memorise the Qur'an for quite some time now and InshaAllah I'll be starting soon. One of the things I want to make sure is that I do this for the exclusive sake of Allah and nothing else, it would of course be a horrible shame and frankly an insult to use the Qur'an for some worldly purpose.

But the issue I've encountered is that there's a lot of social prestige around being a hafidh, and sadly I'm but a simple human and I get attracted to such things. So my question is how do I make sure I do hifdh for the solely the sake of Allah SWT?

2) Can we gift the reward of memorising part of/the whole Qur'an? Specifically to the ma3sumeen

1) Having a pure niyyah is the key to everything we do, especially our worship. This exists in our hearts and is cultivated by only giving value to Allah and His pleasure with us. Thus, the first step is to increase asking forgiveness of Allah, this is the position of humility. Then reduce the desire for worldly things and the unnecessary company of people, this creates emptiness that is filled with Allah’s remembrance. Insha-Allah this will help along with reading and understanding the Quran.

2) You can dedicate the blessing of that mustahab act to anyone.

The Imams (AS) mention finding a compatible spouse. Is this compatibility confined to only having good religion or are there other aspects to it because when I met this potential spouse she has good religion and a good family but when I asked her certain questions we didn’t have much in common so maybe there is a personality difference.

The traditions say that we should find a believer and someone with good character. Thus, everything else is what we work on together and develop in a relationship. Sometimes there is no connection initially but then it develops. But, if there is too much difference personality-wise and no connection at all then you are not compelled. May Allah give you a wonderful spouse