There's no need to to have the bottom of the tank completely covered unless you like the look of it better that way. I wouldn't stress too much about the pH tester, but you need to test for ammonia, nitrite and nitrate while you're getting started. Read the article on Fishless Cycling that's stickied in the Freshwater - Getting Started forum. You won't be doing exactly what it says since you already have a fish, but you need to understand what's going to happen with your water chemistry here.
With a fish in the tank, you need to be testing ammonia and nitrite daily at the start, and change water as needed to maintain ammonia less than 1 ppm
and nitrite less than 0.5 ppm
before the water change if you want the fish to survive (ie if the fish is producing 0.25 ppm
nitrite daily, you need to change water until the level is less than 0.25 so that it doesn't exceed 0.5 before you come back to test again).
Initially expect to see ammonia rising steadily and nitrite reading consistently zero. After a period of time, usually several weeks, you'll see a sudden rapid rise in nitrite and soon after (1-3 days) ammonia will go to zero. Once you see nitrite you need to start testing nitrate as well. A week or so later, nitrite will drop to zero and you'll see a rise in nitrate. Once ammonia and nitrite are consistently zero your tank is established and you can stop testing ammonia and nitrite unless you have reason to suspect a problem. Continue testing nitrate about weekly. Nitrate is safe for fish up to at least 40 ppm
, and isn't critically toxic at somewhat higher levels. It can only be removed by water changes or live plants.
All the above assumes you have a filter. You MUST have a filter. Bettas don't like current much, so if you can get a sponge filter or something without a lot of directional flow that would be best. Without the filter your fish is virtually guaranteed to die of ammonia poisoning at some point.
Never replace or wash filter pads in anything but tank water.