does it mean that the motor will receive 12V/phase?
Yes, well it can't get more.
Does the driver regulate somehow the output leves or what?
It has a chopping relator so once it reaches the current you have set it cuts off. Your motor is not actually designed to run off 3V3, it is just that the resistance of the coils means it gets it's rated current at 3V3. Powering it from a higher voltage is good as it means it can be stepped faster.
Could I use it simultaneously to power the arduino board and the easydriver?