If I sign this Affidavit am I responbsible to pay her debt? Is there a way to get the money w/o paying her debt back?

You will most likely not be responsible for any of your aunt's debts, unless you were a co-debtor with her in some way. Debt of a deceased person...

Is she qualified to be appointed as executor by court?

The non US citizen executor may qualify to be an executor in NY if she resides in NY. If not there will likely have to be a co-executor appointed....

Parents' will requires I divorce my spouse, I did after their death, am I in the will?

The clause will likely be voided by a judge for being against public policy.

Relocation in New York is a complicated issue. Agreement in writing by the non-custodial party is the less complicated solution. However, you may...