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?

1. yes.

Yes, but I wonder why you're asking this: ordinarily you get to keep any tophies of monsters you kill during encounters, just like any other combat.

oops, didn't notice this was asked a few times and already answered here