Will bunions (tailor's bunion/ bunionette) fully heal?

Yes: If you are talking about after a surgical correction the answer is yes.

Depends: Bunions, tailor or otherwise, don't disappear or "heal" untreated. They tend to enlarge over time. Bunion surgery does heal, faster if post-op instructions are followed. Healing rate varies with procedure, but if a bone is cut and straightened, figure on 6-8 weeks before you are back to most shoes and activities.

Usually yes: On occasion people may get a recurrence.

Surgery: I'm assuming you mean after surgery. Yes they should fully heal, depending on the procedure and how much you were on your foot after surgery 4-12 months for all the swelling to dissipate.