Can you play local or and online? Do you have to do anything to make it work? (since I guess the servers are long offilne)

Multplayer should work out of the box, GOG already provided the IPX wrapper DOSBox script as with other releases that need this (i.e. Master of Orion 1+2). As the DOSBox IPX wrapper converts the network packages to standard TCP/IP, so you can use something like Hamachi to play online.
If I remember correctly the game modes were standard stuff like Deathmatch and CTF, but it has been a long time since I played Carmageddon Multiplayer.

Awesome, thanks!