How can my wife travel outside the U.S. with a pending I-539 application and a pending EB-5-based I-485 application?

It appears there are two dilemmas. First, your I-485 has been filed and any travel without either an approved travel document or the requested change of status from B1 to F-2 will result in treating the I-485 filing on her behalf as abandoned. Secondly, to have a valid status to return into the U.S. upon her travel, she needs to wait, process and obtain approval of her F-2 while in the U.S. Thus, she needs to stay in the U.S. and not travel.

It might be best to wait until her application to change status is approved. She must be in status at all times before filing. Since the change is deemed abandoned if she leaves, it is prudent not to travel at this time.

She cannot until she gets advance parole (travel permit). If urgent, demonstrate the urgency for an emergency permit at an INFOPASS appointment.

Your wife may be deemed to have abandoned her F-2, but can re-enter on her AP. As an applicant for adjustment of status, she can attend school.

A change of status application is usually abandoned upon leaving the U.S. She would re-enter as a pending immigrant under the pending I-485 for her. But the act of filing the I-485 could also result in the I-539 being denied anyway.

That is correct. If she departs the U.S. while a change of status application is pending and re-enters on the AP, she will have abandoned the change of status application.

Yes, leaving the U.S. abandons an application for change of status.