Learn Swedish: Gör bedövningen ont? - Does the anesthesia hurt?

It comes from the verb att bedöva, which means to numb or anesthetize. By dropping the final -a and adding the suffix -ning, it becomes the noun en bedövning (anesthesia or a numbing). Here it is in the definite form, bedövningen (the anesthesia).

Why does the sentence use gör to mean hurt?

In Swedish, the standard way to say that something hurts is using the fixed phrase att göra ont (literally to make bad or to do pain). So Gör bedövningen ont? translates literally to Does the anesthesia make pain?

Why are gör and ont separated from each other here?

Because this is a yes/no question, the main verb gör must come first. The subject bedövningen immediately follows the verb, pushing the rest of the fixed phrase (ont) to the end of the sentence.

Are all nouns ending in -ning treated as en words like this one?

Yes! Nouns derived from verbs using the -ning suffix are always en words (common gender). That is why the definite form here is bedövningen instead of bedövninget.