My current system uses a 20-25 foot component cable from A/V processor to ceiling-mounted projector (plus a few additional feet of connecting cable from sources to processor). I plan to upgrade to HDMI components, but can I use an HDMI cable of this length?

Yes. I use a 35' Monoprice 22awg HDMI cable from my Onkyo TX-SR805 to my Panasonic ae1000u projector. Never had a problem. Not too shabby for $60.

If for whatever reason you did have a problem, you could get an HDMI booster, but you shouldn't need a booster for anything under 50'.

Yes you can. With length you may run into problems, but that's not super long.