What makes you think he was "off duty?" As mentioned, he may have been a detective, a supervisor, or even a manager (i.e. a lieutenant or higher) and not working a uniformed patrol assignment. Most "off duty" officers don't have personal cars with emergency lights in them.
So, he may not have issued the cite himself because he didn't have a cite book, he figured he needed to chill after your 'tude, or any one of a number of other reasons.
Didn't you get this info?2. When asked arent officers supposed to give there name and badge if it isnt on the ticket?
They don't have to drop what they are doing and give you that info, no. Such side questions are also common distraction techniques employed by some criminals to try an distract an officer and change his focus or put him on the defensive, thus letting down his guard. An experienced officer shouldn't play that game.
The issuing officer may not necessarily be the "arresting" officer. if you take the matter to trial and the issuing officer appears and tries to say HE saw the violation, you can object and point out that it was another officer who did. I suspect, however, that the other officer will appear in court to testify as to what he observed.3. is the ticket for running a red light valid, if an officer that didnt even witness the violation issues me the ticket?
You're lucky the officer did not direct you to step out of the car - something he can do, and you would have to comply. The window thing can be annoying and the way to get around that is to bring the driver out of the car and back to yours. The fact that the officer did not play that card shows that he was rather patient with you.
And while I can understand some measure of reticence regarding a stop by an unmarked vehicle, it WAS (I presume) in a very public place. But, if polices are the same there as they tend to be here, the non-uniformed officer should understand the request and have a marked unit respond. Which, he did. You do not necessarily get to have a supervisor, respond, however. You are certainly free to go to the station and talk to one.

