I hope you don't take this the wrong way, but head and tail light tetras aren't really suitable for a tank of that size. They are a shoaling fish and should be kept in groups of at least six, and that would leave you massively overstocked, I'm afraid. I would rehome them and think about getting something more suitable (male Endlers or guppies, a single Siamese fighter, ember tetras or microrasboras all come to mind).
There's no way of knowing whether your tank is cycled, or whether it's safe to add new fish, without testing for ammonia and nitrite.
As to water changes. Weekly is best and the amount depends on your stocking. The best guideline is to see how high your nitrate rises between water changes. Start off with 25-30% weekly, but if the nitrate goes up above 20ppm more than your tap water, you'll have to do larger or more frequent changes.