With a yellow crowbar, obviously.

He would become Black or Yellow Lantern, I think. Otherwise, Idk.

Laughter would be something like happiness, right? I suppose Joker could be in line to be a Gold Lantern

Plus didn't a former Gold Lantern lose his sanity?

Plot Induced Stupidity.

Easy, Joker becomes a Yellow Lantern or gets a connection to the Negative Speed Force and then uses Joker Gas, I'm Also Pretty sure Joker has defeated Hal in the Comics (Correct Me if I'm Wrong)