1) Absolutely not. One fancy goldfish reaches 8 inches or more and needs at least a 20 gallon tank to itself. Ghost catfish are tropical fish whereas goldfish are cold water fish, so they cannot be kept together; you're looking at two tanks.
2) For two tank setups, several hundred dollars at least. If you were to set up a 20 gallon kit for each (about $80 per kit) you'd be looking at $200-300 or so by the time you added everything else you needed. (Gravel, plants, water conditioners, nets, food, etc.)
3) Goldfish should eat goldfish flakes, with other things occasionally as treats. The catfish would need tropical flakes and/or sinking pellets.
4) For the catfish, 75-80 degrees. For the goldfish, I've heard 68-70.
5) Yes, the tank still needs to be cleaned. For a tank with a ghost catfish, 25% once a week using a gravel vacuum is fine. Since goldfish are messy you need double filtration (for the hypothetical 20 gallon tank, 40 gallons worth of filtration) and also need to clean the tank every week. If you don't have double filtration, I'd say either 25% twice a week or 50% once a week.
It's great that you're willing to give these fish a home, but they are two different fish with very different needs. They cannot be kept together, so if you're not interested in setting up two different tanks then you might want to take one or the other in a 20 gallon. Keep in mind that in addition to growing to 8 inches or more, fancy goldfish also live ten years or more and are a long-term pet. Good luck! :)