Does the Metaverse allow you to play with other people or just yourself?

It's more like an online scoreboard or highscore list, you play the game just as you usually would only using the metaverse option to start(you'll need to create a character). Upon completion of the game it will ask you if you'd like to submit it to the meta.

There is no multiplayer. Metaverse games are games you play by yourself that get listed to a common scoreboard as DethAdder mentions. You can compare your performance to the performance of others but there is no multiplayer in GalCiv2.

There is a way to use cheat mode to play a hot-seat quasi multiplayer game but IIRC it doesn't really allow both players to play on an equal footing. I forget exactly what the issue is. It basically involves starting a game normally and then one player taking over for an AI. I've heard of this as a possibility but never heard of anyone that has ever actually done it.

Request for multiplayer support is a topic that has been done to death around here. There is an "official" thread (I think it's stickied) somewhere that should be easy to find in a search if you wish to pursue this topic, however as I mentioned it's a topic that has been done to death.