Can you still get dentures if you don't have any gums left?

Yes. Gum tissue can be added or transplanted to the deficient areas from the roof of your mouth which is a replenishable source for the gum tissue needed to support your denture.
Yes. Implant overdenture on dental implants. The implants will help stabilize the denture.
No. Dentures need to sit on or be anchored to something...If no mandibular ridge, hard to do. Uppers will certainly have maxillary structure. You need to see a dentist that fits dentures to determine your options.