If Arkham is at it's monster limit and a monster flies to the sky (which is included in the limit) does this monster stay in the sky or go to the outskirts (because Arkham is now over it's limit)? I can't see anything in the rule books that covers this. The question probably applies to swimming monsters too (Though I haven't used those yet).

The Sky is part of Arkham, monsters there count against the monster limit. Hence, if Arkham has already reached the monster limit, a Flyer moving to Arkham is moved to the Outskirts instead (normal rules for Outskirts limit and terror increase still apply)