I believe you will find your problem originates with the lens.
Change to another lens, I'll bet your problem won't repeat on another lens.
Sometimes a CLA of the lens will correct, at times, a new shutter or replacement shutter is called for.
Wear within the shutter can cause the flash to fire upon opening, and again when closing.
In your situation though, all bets are off, as you also describe a non-functioning hot shoe.
Time to have your camera body, and the suspect lens CLA'd.
The hot shoe is only an extension of the lens' flash circuit; no different then an extension cord for a table lamp.
If you have a fault in any part of the extension cord, the table lamp won't work.
Because of the bellows focusing, you actually have a built-in extension cord, of sorts, connecting the gold contacts on the face of the movable lens board, to the stationary camera body. This cord, or cable strip, moves in and out, under the bellows-rack/mirror-box, as you focus in or out, (sort of a, rolling-fold).
A couple of the gold contacts, (interfacing lens to body), at the lens mount, carries the closing of the flash circuit, from the lens to the hot shoe, via the cable strip when the lens fires.
Nothing in the camera body influences/triggers the hot shoe, except needing good contacts on the gold pins at the lens board, (lens mount/camera body interface), and a cable strip w/out any breaks/shorts.