What causes these spots at back of tongue and mouth?

What type of spots: Generally people that have spots on the back of the tongue need to brush their tongue or use a tongue scrapper/cleaner.

Taste buds: More than likely what you are seeing are the folate (folic acid) papilla, a type of taste bud on the very back surface of your tongue. The are larger and more pronounced than those on the front of your tongue. Of course without a picture, we have no idea what you are talking about. I would have your dentist evaluate the spots to rule out any pathology.

Hard to tell: Without seeing your tongue it is hard to determine what is going on. It could be normal or some sort of condition needing treatment. I would suggest seeing a dentist for an evaluation.