What kinds of lightsabers (and fighting methods) are available?
Number of light sabers depends on your advanced class.
Jedi Guardian - Sith Juggernaut - 1 Lightsaber
Jedi Sentinel - Sith Marauder - 2 lightsabers
Jedi Sage - Sith Sorcerer - 1 Lightsaber
Jedi Shadow - Sith Assassin - 1 Double
So no, you cant have 3 lightsabers on the same fight.