Probably not good for a seedling. You should harden them off inside first, or put them in the shade for a few days. Then move them to partial shade, then finally full sun. I've grown in weather well into the 100's with humidity to boot. Your plant won't mind it, in fact I think they grow better, but you won't like the watering it takes.
Could be transplant shock. I'd wait until they've got 3 pointed leaves before I do any transplanting. If you shock them that early it tends to be disaster. Hard to say about the cotyledons could be a number a things from over watering to nutrient burn. If you could get a picture would help, but you're probably better off starting some more seeds.