Is it permissible to distribute the raw meat of the vowed animal sacrifice amongst the poor/to offer it to them in cooked form?
It is impermissible for the vow-maker to eat from the vowed animal sacrifice, rather, he/she should distribute it as he/she had intended upon making the vow, but if the vow was a general one, without any specification then, it is better to give it as raw meat.
Should one who doesn`t perform prayer out of laziness make it up later, and how should he/she do so?
All perfect praise be to Allah,The Lord of The Worlds He/she is obliged to make up missed prayers by offering with each obligatory prayer another one, and if he/she offers two, then it is better. And Allah Knows Best.
Is Buying a house in installments through banks?
Taking a loan from interest-based banks is prohibited and considered a major sin. Instead Getting a loan from Islamic banks is considered Murabaha and can be used as an alternative, provided all the necessary Islamic conditions are met. And Allah Knows Best.
Is it permissible for someone to make a supplication to Allah to marry an already married, or an engaged woman?
No, it isn`t, and the person who does so is sinful before Allah, The Almighty.