For all those of you who'd caught Beverly Hills, 90210 during its entire run on FOX from 1990-2000, can anyone pinpoint exactly whether or not the pilot episode that aired 10/4/1990 used the John Davis theme or if it had used the rarer theme co-composed by Jeff "Skunk" Baxter and Stacy Widelitz?

The Baxter/Widelitz theme song was only used on the episodes whose opening titles had the credits in pink text, which again only applied to episode 2 and maybe also episode 3.
https://www.youtube.com/watch?v=c549DnkMAfQ

Also, did seasons 2 (1991-92) and 3 (1992-93) use the same exact title sequence and the remixed John Davis theme (likewise, didn't both seasons 4 and 5, from 1993-94 and 1994-95 respectively, use the once-again-updated Davis theme song)?

Getting to season 6 (1995-96), this theme was shortened to remove the second guitar stanza and the subsequent first saxophone stanza.

Season 1 (pilot and all other episodes except 2-3): John Davis theme (version 1)
Season 1 (episodes 2-3): Baxter/Widelitz music (opening title with credits in pink text)
Season 2: Davis theme (version 2)
Season 3: (same as season 2)
Season 4: Davis theme (version 3)
Season 5: (same as season 4)
Season 6: Davis theme; shortened to go straight from the first guitar stanza to the second saxophone stanza.

~Ben