I hate soldering guns, they are horrifying an nasty things. Why aren't you able to do the lineman's splice? Better question, why would you want to???
1)What gauge wire do you use?
22AWG? for the individual lights at least, It's smaller than I would like, but it works and doesn't heat up.
2)Attachments to heatsinks?
Loctite Stick n seal
3)solder first or when attached?
Well both... What? Reflowed the LEDs and drivers onto the PCBs, glued those onto the heatsink, then soldered up the assembly.
4)type of solder/irons
Cheap 48W adjustable thing from Amazon.
5)Best heat sinks as to material/cost/availability/scrap
I just used some 1/16" aluminum pattern mesh, it gives me lots of room for airflow, and it dissipates heat quite well.
My light technically isn't adjustable, but with some work it could be. It's not an especially electrically elegant setup, but it's really receptive of modification and adjustment, not to mention how stable it is.