Who removes old questions?

They don't get removed UNLESS other users report them enough as violations, to get removed from the display. The purpose of this site originally was to become a database of information/experience for anyone to access. With that in mind, removing questions takes away from that. 

.

Users who post questions cannot remove them if the question has any answers. The only way questions are removed after receiving at least 1 answer, is if they are reported enough to be removed. All the questions posted by a user will remain in their YA activity as long as their Yahoo account remains active. Even if they close their Yahoo account, all their posts remain on YA. 

In principle, it doesn't get deleted at all. That way, people in the future with the same question can find the answer in seconds instead of wasting our time and waiting for hours or days.

It stays there forever, you can only delete a question before it receives it's first answer (unless it was reported & got taken down.) You can't delete questions that have been answered, even after favourite answer is awarded... and I wouldn't bother reading the terms & conditions because some of it is outdated & some of the rules were changed but the terms & conditions never talked about it.

It will never be removed. Questions are open forever and can continue to be answered even after a Best Answer has been chosen.