I have had painless white stuff on back of tongue and swollen taste buds for a few months. I think it is thrush. Will gentian violet cure this?

See a doctor. You also asked about gential violet for vaginal yeast infection. See my reply to that question. Oral thrush is uncommon in otherwise healthy persons. "Painless white stuff" usually isn't yeast (thrush), just a garden variety "coated tongue", which can occur with colds and any number of minor health issues. Don't use GV, which isn't recommended for oral treatment. See a doctor for both problems.