Can soft tissue grafting get paid by medical insurance instead of dental, since it's oral surgery?

Depends. It depends on your particular plan. Most "dental" procedures such as grafting are covered under dental plans and not medical. The only way to definitively find out would be to send in for a predetermination.
Not likely. Most medical plans simply role out dental procdures.
Not very likely. If it's a true skin graft, it might be covered by medical insurance. But if it's a gum (gingival) graft or a subepithelial connective tissue graft, it's a strictly dental procedure and should not be covered by medical insurance. However, dental insurance should cover it. Don't forget you'll still be responsible for your deductible, coinsurance and for non covered services.
Not usually. Soft tissue grafting is classified as "periodontal surgery." most soft tissue grafting in the mouth is performed by a periodontist to help repair and replace lost of damaged gum tissues. It can be "covered" on dental plans at either 50% or 80% levels, but it is usually not covered by medical insurance. I hope this helps!