It depends on the circumstance. A ball can be thrown with a glove to a base in an attempt to force or tag out a runner. A ball can be thrown to a cutoff man with a glove. However, a pitcher cannot pitch with his glove.
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If you are talking about a runner trying to score from 3rd. base yes, you can, (in most leagues, Little League and younger they may have added specific rules about this to limit the chance of player injuries.) If you are talking about during an "at bat" no. If the bat touches the catcher's glove on a pitch it is ruled cather's interference. The play is ruled dead and the batter is awarded first base. And no, I have never seen anybody who could hit a ball out of the catcher's glove and NOT touch the glove.
Yes. In the rare case that a batted ball gets stuck in the webbing of a glove a fielder may throw the glove to another fielder when attempting to put someone out.
It is not allowed! Some players would put a substence on them and cheat, or some gloves are better than others. It can easily alter the affect on the ball when thrown so they are not aloud.
Nothing. He is only penalized if the glove touches the ball. If the glove does touch the ball it is a three base penalty from the time of pitch.