We've come up with two questions that we haven't been able to find answers to:
1) What is needed for a player to get an explored counter when he/she returns from another world? Is it neccessary for the investigator to go through both parts of the world and then come back or is it enough to be sent back earlier?
Just come back... Honestly, we've never ever used these in the 3 years I've been playing AH with my gaming group...
2) After returning through a gate with a monster and sealing it with an elder sign, will that affect the monster (kill it?) or do the investigator need to deal with the monster? Also, can monsters enter locations that have previously been sealed with elder signs or do they lose their movement?
No, the elder sign doesn't affect them. They will ignore you the turn you come back from the outer world, though, regardless of whether you seal the gate, with or without the elder sign.
Additionally, nothing prohibits them from moving into a location with an elder sign, other than the fact that normal movement will never let them enter a location.