I want to buy a house by having a loan from a bank?
If taking a loan from usrious banks it is impermissible; on the other hand, if this took place through Islamic ones then it is permissible to get the loan, since Allah the Most Exalted Said (What means): "And Allah has made buying lawful and forbidden usury (riba)." And Allah Knows Best.
A person vowed to slaughter a sacrificial animal. Is he permitted to eat from it?
If the vowed sacrificial animal was for the sake of Allah, and the one who vowed didn't specify then its meat should be distributed only among the poor and needy similar to distributing Zakah of Al-Fiter so neither him nor his dependents permitted to eat from; however if his vow was to made a banquet and invititing his relatives and others; then he must bring up as much as he can from its meat for them. In addition, he is permitted to eat from it in a reasonable basis. And Allah Knows Best.
Is it correct that everything dry is pure even if it has impurity on it?
If something impure becomes dry, it remains impure and is not purified by drying. However, the impurity does not transfer by touching it if the one touching it is also dry. And Allah the Almighty knows best.
Is it permissible to pay the expiation of an oath to a charitable party as it feeds the poor and needy such as Tkiyet Um Ali?
There is no harm on authorizing someone to handle the expiation of another to the poor and needy, since Shafiee's jurists stated that authorizing someone for the purpose of distributing Zakah, expiation and vow is permissible as stated in [Mughni Al-Muhtajj,vol.3/pp.237]. At last, the intention of the person who intends to authorize someone else suffices in this regard. And Allah Knows Best.