International Institute of Cricket Umpiring & Scoring
'Caught' off glove
"The bowler charged in and bowled a quick bouncer, to the opening bat who took one hand off his bat to protect his face. It was just as well he did, since the ball struck him a nasty blow on the glove, right in front of his nose.Two questions - if someone had appealed, could he have been given out for Handled the ball, and if a fielder had caught it off his glove would he have been out Caught?"
No, to both questions.
According to your description, this was not a 'wilful' act of handling the ball. The batsman was trying to protect himself from injury, which is allowed.
He can never be given out Caught if the ball bounces off a glove that is not holding the bat at the time. Hands and gloves are only a 'part of the bat' for as long as they are in contact with it.
Read more about Law 6 (The Bat) and Law 32 (Caught) at the MCC website