Hmmm... nothing we can't fix. Just keep the water very clean (keep the water parameters good in and tip top shape) and it should heal on it'd own. If it doesn't heal within 2 weeks, I would treat with MelaFix. If after that nothing gets better,
then I would move to the larger meds like Maracyn I.
This is probably just run of the mill fin damage. If there an ornament in the tank that could have done this? Goldies get caught on the silliest things.
About the eating, try feding peas. Most goldies love peas. De-husk them and make sure they are not frozed. Just throw them in the tank, they usuallt gobble them right up... although... my fish hate them!
Anyways, try the above and see what happens. Things should improve. Also, be sure to soak all the food you feed them. Pellets, flakes etc... goldies are prone to swim bladder disease and so the excess air should be taken out of their food by soaking it in water first.
Keep is posted and good luck!