Welcome to the forum!
Yep, you can certainly do that.
No, but you can make it work. I'd suggest using the speaker-level binding post outputs from the amp (not bridged, if I'm understanding your set up correctly), run both the right and left speaker outputs from the amp to the speaker-level inputs on the sub, then run the speaker-level outputs on the sub to the speakers. I've never done speaker-level to 1/4" connectors before, and I'm not very familiar with PA speakers, but it seems that the 1/4" inputs on the speakers are for speaker-level power - so I think it would be okay.
I sure hope someone else chimes in on this, though. I'll report back if I do more research myself.
Yep, you'll control the crossover using the subwoofer.