You should definitely be testing for ammonia, nitrite, nitrate and pH. If they are all fine then there certainly is no need to mess around with them - apart from your weekly water changes of course to remove nitrate - but if they
aren't fine for some reason then you will have no way of knowing what is wrong. The water is the most basic of a fish's needs, and it must be right if they are to grow and thrive.
The fringed tail is actually a sign of finrot, which is usually caused by poor water quality. Test the water and let us know how it's looking. You may need to use salt and/or an antibiotic to cure the finrot.
Hope this helps.

EDIT: I forgot to add that you don't need to use Cycle if your tank is functioning properly.