[MunchkinMan]

You roll for that Monster and can affect its sure roll with that affect your or any die roll. Other players can affect it with cards that affect someone else's or any die roll.

You can't Run Away before combat starts in Munchkin, so I don't think there is any divergence between the two games...

You can search in a room with another munchkin, just not where there is a Monster. If you find a Monster while searching, any other munchkins in the room do not automatically join in the fight, but you can surely ask one to help you, if you need it.