As far as your game question, from what I've seen, each device stores it's own data. No way to share data like that between devices. It's a privacy issue I guess. So each game would start fresh on each device. I was trying to find a way to share data stored in an app between my devices, and was told it was impossible.
As for the Apple IDs, I won't say for certain, but I believe if you have 2 Apple IDs, all purchases are kept separate. I think you can only be signed into one Apple ID at a time on a computer. So you would only see apps purchased with one ID at a time. No way to share apps that I know of. Multiple Apple IDs make things very tricky. Even when iCloud came out, I had 2 IDs. And even though all my purchases were on one, and my other was just from MobileMe, it was Hell trying to figure out how to merge them. Had my apps on one, and my contacts and calendars on the other. Apple said it couldn't be done. Then I figured out a way to do it. Single Apple IDs make life a lot easier, but that means you'd have to rebuy all your apps over again on one of the IDs.