1. If you defeat any monster that gives items such as the mi-go, warlock, etc., do you get these items even though you do not get to keep the monster as a trophy, when in the Other Worlds?

With those monsters you never keep them as a trophy. If you pass a combat check against them in an other world they will still be returned to the box and you will still get the applicable reward. If you pass combat checks against other monsters in other worlds you do gain the trophy.

(nitpicky PS: you could get them as a trophy with Yorick drawing them at the start of the game, or with an encounter that instructs you to draw a monster from the cup and gain it as a trophy.)

EDIT: Whoops! Taurmindo and Tibs already got this in another thread