We always recommend new caps if they're original.
Might be a problem with the green gun(#1), transistor might have shorted making it on all the time.
Phillips (#2) does not make arcade monitors, but they do make tubes.
(#3) don't replace the whole monitor, just get a new tube! 4600s are awesome monitors with great pictures. As for the missing red, it could be several things, from a blown drive transistor on the neck board to a loose connection to a broken solder joint.