I do not believe "Vanilla Q3" supports what u want. Both Rocket Arena and CPMA do (not sure about CTF mods).
For Rocket Arean it's : /model Crash <----u and ur team
and /enemy_model Tankjr <----the other team model
/enemy_model always works, if my team does not, I type "/model crash" and "/model Crash". Yes, for some reason typing with and without Caps makes a difference.
For CPMA (it's supports DM style and Rocket Arena type play),
See here for a great guide for most/all it's settings including ur questions about Models.
BTW: vanilla q3 means, no mods, q3 straight from "id software", which I doubt many play.