Yes, the bacteria that everyone talks about that is good for your tank (it consumes the waste products put off by your fish) grows mostly in your filter, probably in some sort of little sponge for you if you have a hang on back filter -- that sponge is considered filter media -- tanks that have been running with fish in them for awhile have already established a colony of bacteria in the filter and that bacteria goes to work consuming the ammonia that your fish put off.
The good bacteria doesn't live in the water, however the concentration of ammonia in the water continues to build, especially rapidly with goldfish. That is why you can change the water 100 times a day and it doesn't do any harm to the fish because you are actually removing the toxins from the water but not the bacteria from the filter. In time you will have enough bacteria in there to consume all the waste the fish are putting off and that is when your tank is considered 'cycled.'
After that, you don't have to be as diligent with testing and everything, and you can slow the water changes to maybe once every 7-10 days, changing about 50% probably since you only have a 38L and it won't be a tall task. For now though, I agree 100% with everyone that you should be doing AT LEAST a 50% water change daily, if not more.
When you put the fish in the new tank, your cycle will start over if you begin using a new filter. You may want to get a mesh bag from the pet shop and put the filter media from your older filter in there and place it in the tank near the filter input --- that way you are at least 'seeding' the tank with some beneficial bacteria.
3 pellets per day will by fine, yes, and you honestly may want to only feed 2 per day initially as it will slow down the amount of waste put off by the fish and keep ammonia levels lower.
Once you are cycled, yes, you can add more fish
Enjoy your tank.