Yes the waste is very impressive. I remember when my son's turtle was about the size of yours and I saw her poop. Wow!
Biting air bubbles is pretty normal in my experience.
Turtles need the UVB when they are basking, and only during the day. You're replacing the UVB they get from the sun.
The main site has some great info on basking/lighting.
http://www.redearslider.com/index_lighting_basking.htmlAnd lots of other stuff.
One minor thing to watch: with a strip UVB, it's possible it can be too close to the basking area and be too strong. I've never had that problem because I haven't used strip lighting. From what I've read, one of the main signs would be eye irritation. If you see that, you should figure out some way to raise the light a bit.
As to the filter, particularly if the budget is tight, you may want to wait and get something oversized. Your turtle will grow quickly the first year or two and that aquarium will need to get bigger. Like diamonbacks4life said, you don't want to waste your money on a filter sized for that tank only to find that tank, only to find it won't work in a larger tank you'll need soon.
But that larger tank needn't be an aquarium. Many have used a plastic bin from Walmart. You want to make sure your turtle has space for swimming. They need to be able to get out of the water completely to bask. They need UVB and heat to encourage basking. The larger the water volume the better, both for quality of life but also because the larger water volume dilutes the waste more, meaning cleaning and water changes don't need to be as frequent. You need a heater to keep the water temp from dropping too low.
You're on the right path. You've found the right place to get help and support.
The only other suggestion I'd add now is to introduce some vegetables now. In the wild, as a RES gets older it transitions from a carnivorous diet to a much more vegetarian one. It's actually unhealthy for an older REs to have the high protein diet a young RES has. Many keepers have difficulty with that transition because they wait too long and then try to convert them.
Keep feeding the turtle pellets, but float some lettuce (green or red leaf, not iceberg) in the tank. It will probably be ignored. That's ok. Fish it out after a few hours. Hopefully, some bites will be eaten. At the size you have now, it doesn't matter if not much is eaten. What you want is to get the turtle used to something besides pellets, so that in a year or so, when you start making vegetables a larger portion of the diet, those vegetables are recognized as food.