Will the CP "eat" your own monsters? So, if you have CP and Cute Beast in play for example, will CP eat CB if your opponent does not have a monster in play?
Yes, the CP effect is not optional and applies to all monsters (not just opponent monsters). That means, if the CP is the only monster in play, it will also eat itself! And in your example, you could also choose for the CP to eat itself instead of your CB!
If your opponent has 2 or more monsters in play and you have CP: who chooses which monster gets devoured by CP?
You (owner of CP) get to choose it.
My friend had CB and CP in play. I had Ghostly Guardians, so the damage from CB would have been reflected. The abilities of CP and CB trigger at the same time ("at the start of your turn"). Will the CP devour the GG before they can deflect the 1 damage inflicted by CB?
As per the priority in our FAQ, the Carnivorous Plant activates before the Cute Beast.
Hehe the Carnivorous Plant can be quite powerful. But timing is important. Since it will eat your own monsters and itself if there is no other target, you don´t want to play it too early.