if your nitrite is .5 after a water change,i am a bit concerned.are you performing the test correctly?
the 10 gallons will have to be upgraded soon. until then,i recommend 50%-75% water changes every 3-4 days with light feedings.
what type of testing kit are you using?drops or strips and brand name.
what kind of filter do you have?
what kind of water conditioner are you using?
as far as the fishes behavior,i think that it stress related.fish often exhibit this sort of behavior when moved to new surroundings.moving them back and forth from different tanks only exacerbates this.
i suggest that you get a liquid ammonia test kit,along with one for ph.
fish-in cycling can be dangerous.you will want to keep an eye on the ammonia concentration in the water,as well as the other values.
i recommend that you keep the tank bare bottom for now.this will make the upkeep easier.gravel is not a good substrate for goldfish.fecal matter and uneaten food can get stuck in the voids between the gravel and deteriorate causing poor water quality.leaving the door open for disease.
when you are ready to upgrade,consult with goldfish keepers on this forum. they will give you suggestions as to what type of tank,filter and other equipment are recommended for your new fish.