No, Joe has not violated any rules.
The correct answer is C. No, because Joe does not have to keep a signed copy in his files.
Joe Broker has not violated any rules by keeping an unsigned copy of the mortgage in his transaction files. The buyer's signature is not necessary for Joe to prepare the mortgage, and therefore he is not required to keep a signed copy in his files.
It is important to note that while Joe has not violated any rules by keeping an unsigned copy, it is always best practice to have a signed copy for documentation and legal purposes.