Invisibility is useful when you want to check out where the monsters are and decide on a strategy, for example if you find a group of minotaur headsmen you might want to berserk at least one of them. If instead you find a lone minotaur lord you might decide to find a suitable place to throw rock blasts at it. There is one place where the easiest method is to walk past several/a lot of monsters, berserk a couple of warlocks and hope there are not too many hydras blocking the way, and then really use the terrain 
. That is somewhat easier if they don't see you coming.
Yes