Question 1:

When playing with the "Dunwich Horror" (DH) or "Innsmouth Horror" (IH) expansions (possibly other expansions as well), it says that the monsters on the DH and the IH board do not count against the monster limit in Arkham, and are never placed in the Outskirts. But what happens when a monster leaves an expansion board and enters the Arkham board (eg. by flying, aquatic movement or special movement (ref. Hound of Tindalos)) when the monster limit is already reached? If there are a number of monsters in Arkham equal to the monster limit, another monster moving into Arkham from another board would then make the number of monsters in Arkham exceed the monster limit. So what happens in this situation? Is the monster prevented from making such a move? Is the monster moved to the Outskirts? Or is the monster limit ignored for such situations, making the number of monsters in Arkham higher than the monster limit until at least one of the monsters in Arkham are defeated or otherwise removed from the board?

Question 2:

Some mythos cards, such as the "Lodge Member Held for Questioning!" card, release monsters into the streets of Arkham. However, what happens when the number of monsters in Arkham is already equal to the monster limit? Are the monsters placed in the Outskirts instead, or are the monster limit simply ignored in this situation?

Oh, and a bonus question at the end: When such a mythos card releases monsters into a street where there is already an investigator, does the investigator have to evade/fight the monster rightaway, such as in a location encounter, or does the investigator wait until the start of the following movement phase?

 In both cases, the monsters go to the outskirts. If this brings the outskirts over its limit, follow the normal procedure of upping the terror level.

regarding your last question, monsters added to the board by a mythos card aren't evaded or fought until the next movement phase. Note that Monsters added by an encounter have to be dealt with right away.

Thanks for the clarification! =) This is how we've been playing so far, so it seems we interpreted the rules correctly.

To clarify further: when an encounter says "a monster appears!" it must be encountered immediately, but is not actually added to the board.

If it says "A gate and monster appear!" then it is added to the board, but you do not encounter it immediately! The opening gate takes precedence and draws you in.