Steiny, your car is a 1978, right? My memory is fuzzy, but I thought the front turn signals were in the bumper, and the front marker lights (parking lights) were both on the side and in the same bulb/socket as the turn signals in the bumper. And I thought the bulb in the bumper assembly was the kind with two filaments: a high wattage one (18 watts?) for the turn signals, and a lower wattage filament (5 watts?) for the parking light?
Taking each of your questions in turn:
1) I thought the marker lights stayed on (same brightness) regardless of whether the turn signals are flashing or not. The side marker lights do not flash; only the front and rear lights flash.
2) Since one side is riveted and one side is screwed, it sounds like the DPO has been in there to fix the PS, but perhaps not the DS. Or mucked it up. First thing I would check is the bulb of course. There is only a single wire (red I think) from the stop light switch on the brake pedal back to the stop lights, so if one side is working and the other isn't, it's almost certainly a wiring issue in the rear, bad socket, bad ground, etc. Second thing I would check is that you are getting 12 volts to the DS rear tail light when you step on the brake. If not, you'll have to trace back as to where the break is. And yes, it is possibly to "rebuild" the tail light assemblies. I've had to do it on pretty much every early model spider that I've had. Disassemble, clean up, and put back together, most of the time with a new way to hold the socket in place (small machine screws). Unfortunately, the Fiat sockets are terrible in terms of corrosion, but you can buy a standard bulb socket at pretty much any auto parts store, but then the challenge is to figure out how to mount it in the light assembly. JB Weld!
3) It should be the same as the passenger side, and possibly even the rear side marker lights. Again, I forget exactly what you have in a '78, but I would imagine it's a standard socket for the smaller size bayonet bulb.
Sorry to not be of more help... One last thing: It's always a problem with an electrical ground.
-Bryan