The drywall on my garage ceiling is sagging badly. Is this because it's too thin (I think it's 1/2" and I guess it's supposed to be 5/8") or is it because of humidity or something else? If I re-drywall the ceiling with 5/8" fire resistant (I think that's the code requirement) should I use some kind of sealer on it?
The problem is because sheetrock does weaken a little over time, and with moisture, but the reason you are seeing it sounds like you just haven't used enough fixing points.
Usually you would fix to joists no more than 24" apart, and separate your screws on each joist by 16", which gives you a structure which can even cope with small amounts of water leakage without damage .
If you have joists already present, then you may be able to push the sheetrock back up and nail it correctly, however it may already be permanently warped - this will depend on just how far the bowing is.
I would guess though, that you don't have joists at that spacing - otherwise the sheetrock would probably be fixed to it already - so you will want to remove it all, fix joists and use new sheetrock. (This will be a fun job - especially if the existing stuff is a bit damp - bring friends to help bring it down otherwise you will have an exceedingly messy afternoon)
It sounds like whomever framed your garage might have been extraordinarily cheap and inept by not spacing your ceiling joists 16" apart on center. A full sheet of drywall is hung securely either horizontally or vertically on 16" centers.
If it is not this then the people who did your drywall were extraordinarily lazy by not hanging it correctly. They might have just nailed or screwed in the sides and corners and neglected or ignored securing to joists running through the middle.
All garage ceilings face a 9 out 10 chance of distortion or failing completely if there aren't ceiling battens fitted to the joists, as this creates a braced grid type situation. Screws won't hold the ceiling for much and can be no help as stud glue gives a better strength hold.
I guess you can put in a ton of screws, but glue in my opinion would be best applied prior to any rescrewing of plasterboard. Garages are cold and damp and don't often have carpet or heating so an interior plasterboard can suffer more than a interior of a home ceiling with insulation also. The dampness is the problem.