Which order should I schedule my surgery (LIPO/stomach or FUE/edges) ?

If you are planning on multiple cosmetic surgeries you need to plan the order with your doctors who will be performing the surgery. There is no absolute rule.

Hair growth can be effected by many things, probably including anesthesia.  You should not expect the change to be permanent, it may just be slowed.  As long as the follicles that are moved have time to heal in their new location, I would not worry that they are going to be negatively impacted by anesthesia for liposuction.If you are ready for your hair transplant, go ahead.  Decide on the liposuction later. 

There is really no connection between your abdominal lipo and the FUE, so you can schedule whichever one you want first, and follow after a few weeks the second procedure. FUE is relatively completely healed in 3-4 weeks, so anything you do at that time such as your Lipo, can be done after 4 weeks.