There are options for automatically syncing apps and such, but you can't stop it from downloading updates. It doesn't download it right away. If you don't update for a little while after one is released (like a few days I think, not sure), then it downloads the update, if connected to WiFi, then tells you and badges the Settings icon so then you would just have to install it.
Yeah, only over WiFi. Even if there was a setting, it's more likely it would be on the phone rather than iTunes due to the fact that devices are PC free with iOS 5.