I haven't been getting emails unless I go in and physically check my email so do I need to have service books sent?
It's not just the app but the account that matters. You can't make a non-push account push.I believe the default e-mail app is not instant/push e-mail, which means your phone would only check for new messages every X minutes or whenever you manually check.
It's only push between gmail and the device though. Again, you can't make a non-push account push. Gmail's mail fetcher runs on its own polling schedule but one plus of having gmail poll is that you're not wasting your device's battery life since your device isn't constantly polling your mail accounts. It's about as close to BIS as you can get in the Android world.There is actually a way to have gmail push your other mail accounts to your phone. I believe the article was on this site. Just search for it and you should find it.