I fought Diablos as soon as I got him too. I went back to Balamb Garden and saved by the directory and beat him. He was pathetically easy once Selphie blinded him. The whole battle I was sitting there testing magic Selphie got on her Slots while all of my characters had 1 HP.

After I had Diablos beat I went up and won Seifer's card from Cid.

I'm not sure when I first fought a T-Rexaur. I think I fought one after I got back from Dollet. I had Shiva at level 100, summoned her once, and then Carded it.