The answer to your first question will depend on which custom ROM you go for. The more established ones will work with at least everything your phone can do on its stock ROM. Newer ROMs may have some teething trouble, but if they're well supported, they'll be quickly fixed.
Updates are manual, but they tend to carry good, transparent change logs so you can decide if it's worth updating or to wait for the next version. Updates are usually much more frequent than those of HTC and carrier ROMS, and the teams behind the custom ROMS tend to release fixes more rapidly, too.
And you won't miss out for long on any official, useful updates. Official HTC firmware and software updates sometimes appear on custom ROMS before stock updates or releases due to developer leaks, e.g. Sense 3.0 appearing on some custom ROMS for the Desire S.