Hey Nyg, welcome to the Galaxy family!
1) The lag is noticeable because you're looking for it. It doesn't feel like a slow phone and if you didn't know about people complaining, you probably wouldn't notice. It's not bad, it's just not the perfect UI people were expecting. In any case, you can 'avoid' the lag if you install a different launcher, but I'm fine with using the stock TouchWiz one.
2) Yes, the phone comes with apps that will use data in the background. Maps, GMail, device/contacts/calendar backups from both Google and Samsung, Samsung's bloatware, carrier bloatware... It's not like it'll chew through your data plan since day one, but yeah, they're there. It even warns you of that the moment you turn on your phone. However, there's a toggle to turn mobile data on and off should you choose to.
3) I still haven't bought a case for mine, but I think I'll stick to the flip cover that came with it for now. But if i were to buy a case, I'd go with a slim, discrete TPU one... I don't really like the added bulk and sheer ugliness of cases like Otter Defender and such. You could also check out AndroidCentral's own products, they're cool! And you get to have Lloyd on your phone!