Add one more thing to the list of stuff I didn't know. If the prosecution pushes for that, will the defense be allowed to bring in any of TM's prior behaviour?
The general rule is that character evidence is not admissible to prove "conduct in conformity therewith." There are some exceptions, though. For example, if the defense presents evidence (usually witness testimony) that the victim had a violent character, and that that is evidence the victim started the fight, then the prosecution can present character evidence showing that the defendant has violent tendencies. Or if the defendant presents evidence that he has good character, the prosecution can present evidence refuting that.
Some past convictions are admissible in the prosecution's case, but generally anything that is not a felony and that does not involve making a false statement will not be admissible.