If his fins are getting ragged, you should probably post a question in the disease section. I can tell you a few things in the meantime.
If you end up taking him out, the easiest way to cycle the tank without a fish in it is to toss a frozen shrimp in the tank. The suggested amount is one shrimp per 10 gallons. You might have to replace it before it's finished cycling.
You should be able to cycle the tank with him in there without endangering his health, but as I said, I'm not sure what the water change schedule should be. I would guess that larger water changes somewhat less frequently would work better.
While you can take excellent care of a betta without a water test kit, they are handy!! The liquid ones are considered to be much more accurate than the strips. The API master kit is the what most people use. You would be able to test the ammonia level in the water right now and know whether it was a problem! I first bought just the ammonia test, but in the end sucked it up and got the whole kit....
Some water has ammonia in it coming out of the tap. In that case, the suggestion is to use Seachem Prime as a water conditioner. It changes the ammonia into something that isn't harmful to fish. Since he was fine for quite a while, that's probably not what's going on, however.
I'm wondering what your ph was/is that the guy in the store suggested trying to change it. Generally speaking, it is usually better to let your fish get used to the natural ph of your water than to try to change it. The swings in ph that frequently result from trying to change it are harder on fish than a high ph. The fish stores usually use the less accurate test strips!!
If you post in the disease section, they will help you figure out if he's getting fin rot or if it's something else. In the meantime, if you suspect ammonia poisoning, you could do one of two things: a large water change or move him to a smaller container where you know the water is clean. As long as this post is, there are some more potential issues that people with ask you about! If you take him out, add a frozen shrimp to keep the cycle going.