As you have already been told, your spouse's I-765 should be processed within 90 days of its receipt. However, as you now disclose that your wife has filed form I-539, it would be advisable for her to wait until her I-539 is processed before filing form I-765. While she may do so at an earlier date, that may cause delays in the processing of the I-765 and creates a possibility that the I-765 will not be properly matched with her form I-539.
EAD (an Employment Authorization Document) has absolutely nothing to do with travel. It relates to being lawfully employed while in the United States.
If your wife's petition results in a RFE, she should provide the necessary explanation of whatever it was that inspired the RFE.
You file Form I-539 to extend or change your nonimmigrant status. If your wife leaves the U.S. while her I-539 is pending it will be deemed abandoned.

