Can she do this

She may not be able to force you - but you should be careful about the possibility of allegations of domestic violence (even if they're untrue.)...

What case is it you want to transfer? If you finalized your divorce in Washington the only thing you need to do is start a custody case in Texas.

My spouse and I have been seperated for 7 years and recently he has been deported. We agreed to an uncontested divorce.

That depends upon your situation. Consult a local attorney before you do something that adversely impacts your future.

In a divorce what could the wife get

To answer that requires a lot more information than what you posted. Discuss the situation in detail with a local attorney.

Spouse got deported and I am filling an uncontested divorce without child support

You can't get an uncontested divorce without your spouse's consent. You should not waive child support without careful consideration - and probably...

In our divorce settlement, do i need to pay her the legal fees she paid for the processing of my immigration documents.

Not unless there's some agreement between the two of you or a court order.

What recourse do I have if assets were not reported in discovery?

What does your settlement agreement or judgment of divorce say? Without those documents it's impossible to be certain. Show them to a local attorney.

Wife filed to withdraw order of protection in Family Court. Can we resume contact, or must I await official word?

If you want to be safe you should wait until the order is vacated.

5 years after divorce can property settlement be changed

Not for that reason.

The depends upon your judge's calendar and how crowded it is. Ask the clerk how far out they're scheduling trials...