What should I do with this broken toilet flange? Is it glued in?
Unless it leaks, or you have access below and want to gut the plumbing, don't touch it; just add a repair ring: (use solid 1/8" steel ones to save space, not the flimsy, flanged type which are overall larger in size; even with these you may have to shim the toilet. I find that grout fills the gap between the porcelain and tile nicely, whether or not the toilet is riding high)

Metal Toilet Flange, Quick Repair Ring (Amazon)