Thanks for everyone that helped. We also faced this issue at work and this discussion helped a lot.
One thing that I found out is that the question's corruption in the database prevents us from editing and deleting it, but not from moving it. So, while we prepare the backups and all we need to go directly to the database, we created a "Garbage questions (don't use)" category below "System" and moved the problematic questions there. Now there's no more corrupted question inside the course's question bank so inserting questions from the bank to a quiz is working. I don't know if there's any adverse side effects to this, though.
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