Sauerbraten is a game that has all of the elements that you might want. First of all, it has a solid single player mode in which you will enconuter and AI with a pretty good level of intelligence. Secondly, the game also has a multiplayer mode which you will also enjoy as you can start a battle with your friends.
There are quite a few levels already designed by the developers of the game but, as it never hurts to add more, you can create more levels using the level editor that is included. This way you can create your own challenges.