Must a bas eball player have constant control of ...

I believe it is a 3 base hit or a 3 base error, one of the two. The batter is awarded 3rd base and all runners on base automatically score

I'm not sure of that ruling. But if the ball hit the glove, but not the ground it would appear to be out. I'm not sure.

 What I do know is that there have been 2 cases where a ball was hit back to the pitcher on a bounce, but because he couldn't get the ball out of his glove the pitcher took off his glove and threw his glove-with the ball inside to the first baseman to get the runner out.

 See this article for the last time it happened.

http://query.nytimes.com/gst/fullpage.html?res=9C01E3DE1239F935A35755C0A96F958260