Lately, this user has been asking a lot of questions, from which many have been downvoted and done have been deleted. This user has 18 questions, from which only 2 don't have an answer, but only a few have an accepted answer.
Example if an unaccepted answer: Is there a solid block that doesn't suffocate entities in direwolf20 1.7.10?
Should I do something when I find such users? Is not accepting answers to my questions bad (against the rules)?
A user isn't under any requirement to accept answers to their questions, although it's certainly encouraged that they do. A quick look through that users posts shows that they do know how to accept answers, and just don't do so very often. As such, in this case, my suggestion would to do nothing at all.
If the user had no accepted answers, though, or was really new to the site, then giving them a helpful nudge can be a good idea, just make sure to be nice when you do say. Aka if they make a comment like "Thanks!", feel free to post a helpful comment like:
If this post solved your problem, then feel free to click that checkmark to the left of the answer. That will let others know that your problem was solved, which makes it easier for future visitors with the same problem to find a solution.
