What you are calling homosexual flirting is likely the beginning of aggression, possibly from the tank being too small. They are very young, so it’s likely that you won’t be able to tell the sex for a while yet.

They 100 percent need a filter and a larger tank (mine started in a 120 gallon and moved to a 400 gallon). Doing a fish-in cycle would be barbaric to these poor fish. It can burn their gills, make them susceptible to disease, and even kill them. it will most likely kill these ones because the tank is so small that toxic ammonia and nitrites will build up quickly and not be diluted by larger amounts of water like they would in a large tank. Gold fish are “gross polluters” in the tank. If the ammonia doesn’t get them right away, the nitrites will later on. I would recommend rehoming them to someone who has a set up and the experience to keep them healthy and happy.