I suspect that part of the problem is incompatibility of the fish. Goldfish and koi are coldwater and the rest are tropical. The goldfish and koi need water under 75 degrees Fahrenheit, preferably between 65 and 70, and the tropicals over 76, preferably 78 to 80. Goldfish need the higher oxygen levels in the cooler water and tropical fish's immune systems will become depressed at those temperatures, making them more likely to get sick. Trying to "meet in the middle" will shorten the lives of both.
It is not a matter of the fish getting along, it is a matter of their needs being different. It's not as different as saltwater and freshwater, but their needs are different. One, the other, or both will suffer. Please, separate the tropicals from the coldwater fish.
Get a heater for the tropicals, and a thermometer for both. At least part of the tropicals lack of appetite is probably from being too cold. If the pellets are too big for the fish to swallow, crush them up into smaller pieces. 30 minutes is too long to leave food in, 10 is more like it.
Not eating in a new tank is fairly normal for fish. They'll eat when they get hungry if everything else is okay(temperature, ammonia and NitrIte levels...) If they have been eating regularly, fish can go two or even sometimes even three weeks without eating.