A: The Keepers offered up for combat have to already be in play in front of someone. You do not have to offer up a Keeper from your hand into the Arena.
When in doubt, the general rule with things applying to Keepers is that the Keeper has to be in play in order to be able to “do things”. Usually that means using special powers, but in this case, being in play is what obligates a Keeper to fight in the Arena. Not being in play frees the Keeper from any such obligations.
If there are not enough combatants (there is only one Keeper in play) that entity simply wins by default. They stick their head in the Arena, see that there’s nobody there trying to kill them, breathe a sigh of relief, and get the heck out of there.