I don't see any reason why you cannot be a treasurer, however, if you are to be in charge of a bank account for the organisation then they may need to do a credit check etc which may flag up the IVA. Don't see how the income matters as it is not your money and you are not getting any credit on their behalf.
There is the potential personal feelings of the other members of the organisation, if you become treasurer and they are not aware of your IVA and you don't make them aware of it at any time and then they find out there may be some unhappy people. No matter what the circumstances around your IVA people can react differently and may fee, rightly or wrongly, that someone in an IVA should not be a treasurer.
Yes - so long as there is nothing in the constitutional paperwork of the organisation concerned which might exclude someone of acting if they are subject to an IVA. Ask to see those documents to be sure.