If you make the most of what you already have, you can only improve your results if you improve your knowledge, skills, technique and experience.
The rest of this answer is devoted to the recording of still images, since the video part is explicitly no longer an issue here. Keep in mind that the 7D does not have a continuous AF area during video recording. The answer to the use of videos is therefore completely different. It would be much better if you check video.stackexchange.com for video footage in this situation.
The entire development of autofocus technology in the last 30 years has been driven by the desire to use it for shooting sports and action with greater accuracy and consistency. Sure, it's nice for other applications, but AF technology was always about sport / action. It was there that the benefits were first achieved, which can then be transferred to other forms of photography.
If you want to shoot sports or action in a low-light environment, you usually use the widest aperture that gives acceptable image quality. This allows shooting with a lower ISO sensitivity than would be the case with a very narrow aperture. The noise reduction required when shooting in a dark environment with very high ISO values, such as: ISO 6400 with the Canon APS-C 7D, reduces the image details so that the entire image appears blurred anyway, even if it is recorded with f / 11. Also note that for 7D full-resolution pictures, the diffraction-limited aperture (DLA) for the 7D is f / 6.9. From f / 11, you can probably begin to see the details that reduce the diffraction effects, even if the image is displayed below 100%.
The 7D has a very configurable AF system. It takes some work and practice to learn how to make full use of it. As with any complex tool, the more options available to the user, the more skills the user must use to leverage those options. It is not the most consistent AF system in terms of image-to-image accuracy, but it is good enough that many photographers have managed to take good action shots.
Canon EOS 7D + EF 70-200 mm 1: 2.8 L IS II, ISO 2500, 1: 2.8, 1/400 sec.
Canon EOS 7D + EF 70-200 mm 1: 2.8 L IS II, ISO 1600, 1: 2.8, 1/200 sec.
If you get the desired field of view with the 85 mm focal length, you should consider an AF lens such as the EF 85 mm 1: 1.8. It's a pretty popular "budget" lens for shooting indoor sports. At f / 2.2-2.8, use this setting with the shutter speed you can achieve depending on the subject's motion, and set the ISO value to the value required for proper exposure. Depending on your post-capture workflow, you can use the power of image processing to get faster shutter speeds than you would otherwise.
For further reading:
When should I upgrade my camera body?
Should I upgrade my Canon housing or lens for upcoming trips?
After 2 years amateur photo buy a new body or a great lens?
Which lens for portraits with an APS-C camera?
Should I first improve my body or my lens?
Choice of lenses Canon 70-200 f2.8L IS II and Canon EF 70-300mm 1: 4-5,6L IS USM
Should I buy a new DSLR with my Point & Shoot or spend the money on a photography course?
What is better than a Canon d1100, but still affordable? (The accepted answer to this page contains numerous links to other related questions that may be helpful in understanding how the photographer contributes to the quality of an image, and also acknowledges that sometimes part of the equipment can be part of the problem .)
Can you take great pictures with equipment that is not that good?
Does a better lens help with fast skateboard shots?
Why are my photos not crisp?
How can I diagnose the cause of the focus problem in a camera?
I have trouble getting sharp pictures when I take a picture of a concert from a press pass
This answer contains a variety of links grouped by root cause, and other questions that address various issues that affect image sharpness.
Much noise in my ice hockey pictures. What am I doing wrong?
Blown out blue / red light, so photos appear blurry
Or you could completely change the system because you misused the wrong lens for what you want to capture.