As to the "partially a lens issue," that's a similar limitation to the camera itself that I mentioned in my prior post. The lens is what gathers light, and you want to gather as much as you possibly can. Problem is, such lenses are costly.
There is a surprisingly low amount of light in the indoor arena you're shooting in. It may look like plenty of light to your eye, but to the camera, it's barely adequate. That's where the previous suggestion for a lens capable of f:2.8 comes in. Even if you don't use it wide open, f:4 is better than the 5.6 or 8 that your posted shots are at. Problem is that fast lenses are expen$ive. Your lens is about 600 bucks new, while a 70-200 2.8 would be over 2 grand. That's hard to justify as a hobbyist. Similarly, a better-performing camera will also set you back a good bit of loose change. A D7200, no longer made but a perfectly valid choice, would be about $400 used. Compared to the D5100, it has 51 focus sensors as opposed to 11. Another step up would be a D7500, still available new, but plenty of used ones out there, also with 51 focus sensors, much better low-light performance than the D5100 and the D7200, but closer to 6 or 7 hundred dollars.
My own experience was seeing my work improve with a camera upgrade more than with a lens upgrade. I had a D5000 for quite a while, Moved to a D7000 and saw MUCH better focusing (39-point system over the 11) along with higher resolution than my D5000 had. I only used it for about four years before abandoning it in favor of a D7200, which I've used since 2019. Each camera upgrade was because I'd encountered situations the current camera wasn't good at, whether it was focusing accurately, low light, or (in sports and air-show shooting) continuous shutter speed, and changing cameras was something I felt was worth it to me each time. Spending money is something only you can decide the value of, but the D5100 is at the limit of its capabilities with what you're trying to shoot, mostly because of only having 11 focus sensors. (When I switched to the D7000 over my D5000, I went from about 50% trash during an air show due to poor focusing to almost 0% focus issues!)
I have a 70-200 2.8 lens but hardly ever use it, I prefer the longer focal length of the my 70-300 4.5-5.6 ED lens.
As for your situation, I still think that your camera, even its focus system is pushed by what you're shooting, should be able to produce satisfactory results. Keep that focus mode in AF-C, shoot in shutter-priority with a decently fast shutter speed, and when you click the shutter, be sure the small square in the viewfinder is on your subject. Also, you can select the active starting sensor with the big round cursor button on the back, if for some reason it's presenting you a sensor near the edge of the frame. If the images are dark, or the viewfinder meter warns you of underexposure, raise your ISO. Underexposure is generally worse than high ISO when it comes to noise in the image.