If an Arkham encounter causes a monster to appear on the board (A monster appears!). Does the monster limit effect it as a normal monster?

For example, if the monter limit is 6 (3 investigator game) and there are already 6 monsters around the board, would the "A monster appears" be put in the outskirts? If so, would it remain there at the conslusion of the encounter (immediatly)?

No. If an Arkham or Other World encounter reads "A monster appears!" then you're supposed to deal with the monster immediately. That is, if you defeat it you keep it as a trophy as normal (endless ability notwithstanding—that monster would go back to the cup). If it defeats you or you flee/evade it, it just returns to the cup. The encounter is isolated and the monster limit is irrelevant.

If an encounter says "a gate and monster appear!" then you get drawn into the gate first, and the monster appears in town and is subject to the monster limit like any ordinary monster emerging from a new gate.

However, if your Arkham location is sealed, then "a monster/gate appears" encounters are ignored entirely.