In order to have get the mortgage and equity lines out of your name, she will most likely need to refinance the property to pay off these existing liens.
The terms of the separation agreement executed in North Carolina will be enforceable by a breach of contract action once the separation agreement is executed, regardless of where you later reside.
Child support is always modifiable. It is unlikely that if you and she agree to a certain amount in your separation agreement that she will be able to immediately have that changed. Typically, there would need to be some change of circumstances warranting a modification in the child support amount. However, if there is a change in circumstances then she can attempt to have child support modified (and the same option would be available to you).
Attorney with Rosen Divorce
4101 Lake Boone Trail, Suite 500
Raleigh, North Carolina 27607
919.787.6668 main phone
919.256.1665 direct fax
10925 David Taylor Drive, Suite 100
Charlotte, North Carolina 28262
704.644.2831 main voice
704.307.4595 main fax
The response posted above is based upon the limited factual information made available and is not intended as a full and complete response to the question. The only reliable manner to obtain complete and adequate legal advice is to consult with an attorney, fully explain your situation, and allow the attorney sufficient opportunity to research the applicable law and facts required to render an accurate opinion. The basic information provided above is intended as a public service but a full discussion with an attorney should be undertaken before taking any action.