[@Zyx] "Peacekeeping" in a very loose sense of the word is probably what most Gods that live in Heaven are engaged in day to day. They are a fractious, overwhelmingly martial, and often short-tempered bunch, and duels among lesser Gods are a common sight. Minor Law Gods, Gods of Justice, Peace, and similar titles arbitrate disputes, end disturbances, and hunt down rogue Gods.

However...

Their standards are are dependent on who/what they swear fealty to. Pantheons are alliances of gods, but function like competing gangs within the city/multiverse. Small pantheons are like street gangs. Larger ones function like the mafia. The biggest serve as the functional governments and organized religions in Heaven. 

So it's fine to say "I'm the god of XYZ" but without support to back it up it's a quick way to becoming "god of being a dead asshole" while someone with connections loots your universe.

I hope I'm getting across what a ruthless place the center of the multiverse is. Literally everything is at stake.

With the seeing the future thing, there is no past or future in Heaven. Time describes a process that happens within universes, Heaven is explicitly outside of every universe. So she has a good motivation for leaving, but she would find her foresight useless within Heaven. 

Seeing the future of the Multiverse requires perfect knowledge of everything that exists, as well as everything that does not exist. The last God that tried it had her eyes burn out of her skull.