I am not an expert, but from what I have read, you should leave your axie in the fridge for at least a week once you have put him in there. Taking him out sooner could add to his stress. Check out the guide to fridging axolotls (sticky at the beginning of the Sick Axolotls section) - it gives you the info you need on this question. If he is constipated or has an impaction, the cold in the fridge should help him to pass it. (I understand that this is because when the axie's metabolism slows down, it empties itself of food so that it doesn't go off inside it.)
On the earthworm issue, my axie loves eating whole earthworms regardless of size. I agree with the comment about the wriggling attracting the axie. My lotl Boris has a wonderful time wrestling with his worm - sucking it in, spitting a bit out, sucking it back in again like a big piece of spaghetti, tossing his head around and leaping into the air. Fun for him, just as much fun for the viewer (me). And as for how much to feed them, this is largely up to the axie. As long as its tummy is not wider that its head, it is not obese. Boris is currently eating two worms for breakfast and two worms for dinner. He is a good size but not fat. He would eat more if I let him - his appetite seems bottomless - but I am monitoring his weight at this stage, as he has gained enough weight since arriving very skinny from the aquarium shop.