Look, I’m just going to let this question go out to the rest of fishblr. I’m sure they’ll take care of you.
Yep, goldfish change color sometimes.
Comet goldfish should get to 8″ long, at least, and often grow to be more like a foot. Bare minimum tank size for one is 75 gallons, and yes, you should have a filter. Just about all fish need filters, and the few that don’t need one will do better with one.
If you’ve just found out that you aren’t properly caring for your fish, don’t panic. Do large water changes in the meantime, try and find a larger tank on Craigslist (good for large cheap tanks) or on sale at Petco, and get a large, strong filter.