To me, this fish looks like it has Ich. Salt looking specks.
And the little worms I don't know an exact name, but they would be a parasite. They remind me of branchiobdellidan worms, leech-like, clitellate annelids, Usually seen on crayfish shells.
A salt dip can rid the little leech like creatures from your fish and help the Ich on the fish to come off. But, Cories are more sensitive to salt, though it seems they can take a salt dip. You will need to do some research about that to be sure how you chose to treat them.
And the tip of the dorsal fin on the first pic fish looks like it has erosion, possibly from ammonia burn.
How long has this tank been set up? Do you know if you have a good beneficial bacteria colony growing in your filter media? Familiar with the nitrification cycle?
More here about that