Mice bite in self-defense when they are afraid, and to send a message that they want to be left alone. If your mouse bites you when you try to handle it, spend more time taming it. You can do this by offering treats if your mouse climbs onto your hand.
Avoid the urge to put your mouse down immediately after it bites you. This teaches your small pet that biting ends handling, and reinforces the behavior.
Mice can be very aggressive with one another. Most fights are the result of territory wars. Do not house two un-neutered males together. Females usually get along with each other, although may sometimes squabble.