Welcome and congrats on the bike. I also have a 92 600 along with it's 94 and 95 750 brothers. Good first bike to learn to wrench on, not overly complicated and most everything can be done with simple hand tools.
1) Idle issue - it is a little reluctant to start up (even with the choke), but this was something that I expected from a 26 year old bike. The bike wants to die before it gets warmed up, but once it is warmed up the idle likes to climb to 5000 rpm. I've heard this is a vacuum leak.
As noted above, check for air leaks around the intake boots, and also around the diaphragm caps on the carbs. Better would be to pull the carb bank, clean and rebuild them if necessary. These old carbs can be a bit finicky.
2) Pulsating brakes - My front brakes pulsate, but the rotors, calipers, break pads, are all new.
Make sure they are properly bled and recheck the torques on your rotors and your rotor runout.
3) Radiator fan - The thing never comes on
May be the thermostat switch is bad, or the wiring to it. These bikes have a lot of wiring issues if not cared for, especially around the plastic connections. Best to take them apart (one at a time) clean them and lubricate with some dielectric grease.
4) The fairings don't line up perfect, I don't know if somethings are bent or if this is normal
All the fairings are mounted via tabs or brackets, simple job to rebend them to get things lined up (as long as the frame is not damaged and the fairings are in ok shape).