ammo chips

I am moving my female betta to a 5 gallon tank soon. (She's in a 1.5 now but it's way too small.) I'm worried that it will be hard to cycle a 5 gallon tank since it's still pretty small. Also, the cycle would be lost after every filter change. I have some ammo chips in her 1 gallon to keep...

My male betta has fin rot and is in a 10 gallon tank. The ammonia level has been a 0.25ppm for a while now and I can't seem to lower it. My tap water has 1ppm ammonia in it, so water changes just make the condition in my tank worse. Because my tank is not cycled, something like prime won't...