If the pitcher is in contact with the runner, the runner is safe if the pitcher drops the ball. If the pitcher is in contact with the rubber, it is a balk if he drops the ball.
If you mean a player on base? When a pitcher drops the ball it is a balk and base runners advance one base.
There is nothing in the rule book that says he can't. So it is not a bulk.
The pitcher had 1 balk this game.
It can't ... a balk can only be committed by a pitcher.
"After a Balk was called on the pitcher, the runners were allowed to advance one base."
Balk
No. If a catcher drops the ball, it's considered uncaught. It counts as though the catcher missed the ball entirely. If a pitcher drops the ball, they may be charged with a balk. Obviously, these situations are rare in MLB and all professional play.
No
There is only one call for a balk. When a pitcher is in the stretch and a runner or runners are on base, the pitcher must pause before throwing to homeplate. There can also be a balk called on the pitcher if he makes a move to throw out someone at first base, but doesn't actually throw the ball. (No fake throws to first allowed!) The last reason for a balk to be called is if a pitcher begins to move his front leg towards homeplate, but does not throw the ball to home. (Or simply pitch to the batter). A balk results in baserunners advancing one base.
Balk
A balk can only be called when the ball is live. If a batter has been awarded time out, then play has stopped, and a balk is impossible. It's safer for the pitcher to complete the pitch, just in case the batter isn't awarded time out.