Council of Elrond

A few questions on playing Characters during the Organization Phase:

1. Can you play Characters at a site (their home site or Haven) that you have no companies at?

If yes to #1,
2. When you play the site card, do you play it face-up?
3. Can the Character move (i.e. play another Site card face-down, other than the one you just put down to play the character) the same Organization Phase it was played?

Thanks

1) Yes, if your avatar is not in play. Once your avatar is in play, he must be at the site or you must play the character as a follower.
2) Yes, face up.
3) Yes, the character may take all normally allowed actions.