Legal Question in Family Law in New York

If neither party to the separation agreement has abrogated the agreement, then the agreement is still valid and can be converted into a divorce.

As for your second question about the house, it depends on the agreed clauses in the separation agreement. If the agreement stipulates to all property purchased after the date of signing the agreement then the answer is no. If the agreement is silent to this then the answer can be rather ambiguous. It would be up to the court. I will say it is most likely separate property but not a guarantee.