Can micro liposuction get rid of my perioral mounds? (Photo)

These can be improved with a combination of fillers/fat, lasers, and skin tightening procedures.  Often chin implants or chin fillers can also help give improvement to the subpar jaw line and chin anatomy. Best, I recommend getting a formal evaluation with a facial sculpting expert. Dr. Emer.

This looks like ptotic buccal fat. If it is you should be able to milk it back up into position and remove it via a small incision inside the mouth. If it is ptotic buccal fat it makes no sense to inject a filler as camouflage.

This can be due to tissue laxity as you have suspected but there are cases where the fat pad of Bichet (lower facial fat pad) can actually herniate.  It can be treated by either intraoral removal if you desire a more hollow appearance here or it can be repaired.  In an MACS lift (minimal access cranial suspension) this fat pad is suspended and the excess skin removed from the front of the ear hidden in the sideburn and inside the ear canal.