Yes, you can create private lobbies/matches.
There are Campaign, Freeplay and Stopwatch mode. They're essentially the same.
In Campaign you play all maps in a set order. If you lose, you play a map again.
In Freeplay, you play all maps in random order. The game rules are adjustable.
In Stopwatch, you play all maps in random order. Every map is played twice, every team has to attack once.
There are no game modes per se. Every map has a series of missions to complete, which are based on common gamemodes.