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Okay, whenever the ammonia gets to 1.0 or above, do about a 50% water change, matching temp and using a dechlorinator. If nitrite gets to 1.0, do the same. Keep nitrates at or below 20. These steps will keep your water from becoming toxic to your fish. When you do a water change, use the siphon to suck detritus out of the gravel, as when that stuff rots it releases ammonia. This would have been the preferred way to get the rotten plant matter out of your tank without killing off the bacterial colonies. If you don't have a gravel vacuum/water siphon, they're really pretty cheap at the fish/pet stores, or you could use a clean piece of tubing if you have any lying around. You should never have to completely break the tank down and scrub it.
Now, as to pH.... Leave it alone. Changes in pH will make your fish sick; however, he can and will adjust to your pH of 8. If you wish to mimic natural conditions, you can put a piece of driftwood in the tank, and that will lower the pH a bit. Make sure not to include any limestone-containing rocks, though, as that will make the water harder and stabilize the pH at the higher level. Throw out the pH-adjusting liquids, though, because using them just puts your tank at risk of having dangerous pH swings.
Your betta would really benefit from a filtered tank. Watch freecycle and craigslist for free aquarium stuff. You should be able to score a filter of some sort before long. Once you get a filter, you can probably do 25% water changes once a week to keep nitrates down to an acceptable level. Until then, test the water every day or every other day for a couple or three weeks until you get a sense of how often you need to do partial water changes to keep ammonia, nitrites, and nitrates in the acceptable range.
Oh, yeah... don't feed more than once a day, and be sure not to feed so much that a bunch drops into the gravel, or you will have water quality problems. Since your little guy started out in a bad way it's doubly important to keep his water in good shape. Once a week feed him some vegetable matter other than flakes, for instance part of a thawed frozen pea (just mash a bit of it between your fingers and drop it in -- no hull), as it will keep him from becoming constipated. He's constipated if he gets a string of poo hanging off him -- blecchh, not very attractive.
ETA: Instead of a frozen pea you could give him thawed frozen bloodworms. Bettas eat insect larvae in the wild, and I've never had one that wouldn't go for bloodworms. But this should be a treat food, not a staple. Betta food should be for everyday feedings.
If you can't get even a java fern to live in the tank, I suggest silk (fabric) plants so as not to tear his fins. He does need something to rest on other than the bottom of the tank, and java fern has nice broad leaves. If the only place he has to sit is on the bottom, he's at risk for fin rot from dragging his fins over the gravel with the fish food and waste in it in between vacuumings. I'm sure you've noticed that with those long, flowing fins he gets tired of swimming sometimes and just sits and rests.
Snails -- it depends on his temperament. I've had bettas who picked snails to death, but I've had one or two that just ignored them.
Here's a website I really like in regard to betta care:
betta care There's lots of good info there.
