I am applying for a provisional patent application. Am I allowed to use problems from other studies in my Background/Problems section?
Yes, but probably not copied word-for-word.
Copying another person's text word-for-word could well be copyright infringement, at least in theory. It certainly wouldn't be a good look. Copyright issues are off-topic for this site however.
However, I can't see that using the problems identified in other studies in your own words would raise any problems. Indeed, it arguably shows that you're solving a previously unsolved problem in the art, which suggests non-obviousness.