I think it might only need internet when you're accessing a new realm for the first time. That's the only time it ever gives me a download message.

I'm using Tyro, Cloud, Tidus, Wakka, and Rydia. The best rare relic I've drawn was a 4-star Diamond Sword. I also have a 3-star Dancing Dagger and a 3-star Flame Rod.

The normal-difficulty daily dungeons are a pain in the butt, but worth attempting.

I've beaten the very first elite dungeon twice now thanks to Cloud. The most recent time I managed to keep everyone but Rydia alive. Salve ftw!