Yes, all six studs should be hot if the first one on left is working.
No, you must loosen the nuts on the lower studs to be able to slide them up and out of bracket.
Yes, jumpering as stated would bypass the circuit breaker on the right.
Yes, fixing the breaker on the right should fix your issues, however I would still be concerned about the large after market wire on top right stud.
After determining it's function, you could install another circuit breaker tofeed that wire. Install additional breaker(amperage needs to be determined based on what it feeds and wire size) jumper new breaker to lower right stud with same size wire, connect after market wire to the other stud.
I wish I new how to post photos for others to see. maybe someone else can do it!