Elf recently gave a pretty clear explanation of Fighter Sweep vs. CAP but I don't recall if it was here or on SIMHQ. If I find the thread soon I will post the URL. Basically, though, I believe that you are correct. The CAP orbit will circle the CAP WP until they engage. While aircraft on FIGHTER SWEEP will begin the sweep when en route to the WP.
ALERT INTERCEPT aircraft will not respond to WEASEL REQUESTS.. ALERT INTERCEPT aircraft will launch only in response to inbound aerial threats.
For Weasels, have a flight with a SEAD loadout which is unoccupied with a tasked mission (i.e. in an Orbit). Not sure if they can be placed on a runway and be available. It is possible..