You're pretty good with your assumptions! Except for having to drain the pool - I've been able to do it 95% of the time without having to get in the pool (draining was never done).

Your old light has a 'halogen' bulb, most of them I've seen are Pentair. If you go with another brand's light, you may need to go to the hardware store and get a slightly longer screw for the 'set screw'

If you pull the lights yourself, don't forget to secure the string to the light cord with electrical tape (and I'll still give you a couple of other tips on pulling and reconnecting a light )