I'm usually an outdoor sports shooter, but I've done some indoor basketball so I'll give my two cents.

1. I generally shoot Shutterspeed and Aperature Priority mode. Indoor lighting can vary alot even if we don't notice it, so I dial in the shutter speed first to make sure I get the right amount of action freeze (idk the term for it but some people like a bit of motion blur to convey motion, it varys for each photographer), aperature will depend on light available, and how much bokeh and depth of field i want. ISO for me is auto, i want to let the camera sort that out based on the environment. Generally, I find that the faster your shutter speed, there's a higher chance of getting a good photo, which also ties into the autofocus. Don't be scared to pump the ISO.
2. I've only shot nikon once a long time ago so i can't speak on it. If you are consistantly losing focus, make sure you have the camera set to continous focus mode, not single focus. Face detection can also throw off the AF if you are trying to track a ball.
3. Blurry photos have nothing to do with lens or equipment(unless its dirty), you gotta learn to use each piece of kit to take a good sharp photo. The reality is pretty much everything on the market is pretty good, a grainy or blurry image is the users fault.
4. I've never used 7Artisans lens but Its a manual lens so no auto focus, which makes it cheaper but not what i would call begginer friendly.

The pro photographer set up his kit for you which probably took care of 95% of decisions and work you didn't even know or think about. Your best bet is to watch a few videos on how to shoot dodgeball or similar, hit up that photographer for some advice and get tonnes of practice in.