Is it permissible to undergo various dental treatments—such as root canal filling, post placement, and crown fitting—while fasting in Ramadan, given that it is not possible to go during the time of Iftar, and does anything reaching the throat unintentionally invalidate the fast?

There is no harm in going to the doctor and undergoing the fillings and treatments mentioned during the day in Ramadan, provided one avoids intentionally swallowing anything that invalidates the fast. If something inadvertently reaches the throat without intention, the fast is not invalidated thereby.