Pinched seal, broke seal, material, corrosion, take your pick. Could be anything. Honestly, the aftermarket kits are just fine. No need to go OE on them. We use aftermarket kits all the time at work.
Those are factory fenders with side markers added in. You can find foglight kits on ebay or other places online. Check the members ride section for ideas
Are you just pulling the trans and supporting the engine or pulling both? All you need to do is remove the tierods fromt he knuckles, pull the axles (including part that connects to back of engine), separate trans from engine (while supporting engine either from top or bottom), disconnect...
Those projector lights have absolutely shit output, I know, I had a pair back in the day. A lip kit like that will definitely clean things up on it. I'd just get a set of ebay or wherever oem black housings and consider doing a retrofit (or have someone do it for you).
You can mount the oem...
Take it off and try bench bleeding it first and yes, you'll need pressure in order for the slave to actuate the shift fork. If you cant bench bleed it, you can try vacuum bleeding the system to pull the air out at the slave cyl.
Couple options -
Replace it with an actual cooler
Get some fittings that will fit the factory hoses and just replace it with an appropriate rubber line.
I just checked, no one in the country has it.
It seems like a very redundant system, cable from pedal to that sensor, electrical signal from that to a control module and relay on the pass side kick panel area.