some gate cards has a "A monster appears!" action. But where does that monster appears? In the other world? And so, do you have to fight it right away or can you evade it? Or does the monster appear in Arkham?

Thx.

They are the same as those encounters in Arkham. Draw a monster from the cup and deal with it as your encounter. If you kill it, you get it as a trophy, if you Evade/Flee/lose combat, the monster returns to the cup.