If the kitty hasn't been de-wormed or de-flea'd when it was in the shelter then you need to get this done asap. The scabs could be from where fleas have irritated the skin and kitty has had a good scratch, especially if it has really sharp claws. If you can get the kitty to the vets as soon as you have a new carrier and then the vet can get scratched giving any treatments

It could be stress related, I have a very nervous cat who is fine around us inside the house but if someone she doesn't know comes around she's off like a shot, when she is stressed she can get runny poops. Hope the kitty gets better soon for both of you (as it's not nice cleaning the tray with runny in it).