How many times can I use The Shiny Orb?
The rulebook (page 14) states that the Shiny Orb can only be used once per turn.  Nothing about per opponent.  You can use it but once each turn.

You can use it in addition to the Vampire power (which can be used once per opponent per turn.

If you are Magic, then you can use it one additional time, on the same or different opponent.