If I get a badge once, can I get another if I do the same thing again?
Say for example the "Stellar Question" badge:
If I have 2 questions favorited by 100 or more users, do I get the badge twice?
You should check the respiective badge's page.
Example, a badge which can be earned multiple times (highlight by me):
However, if a badge doesn't specifically say that it can be earned multiple times, assume it can't:
Depends on the badge. Badges such as Autobiographer(awarded when the user completes all user profile fields) are not awarded everytime the user completes all fields(if he removes/edits any field).
However, badges such as Stellar question (Question favorited by 100 users) awarded to the OP everytime a (new) question is favourited by 100 users.