Indoor badminton live streaming

Hello everyone. I was struggling on whether to put this in the Beginner section or here... so here goes.

I would like to first explain my situation and then get some precious advice from anyone interested in helping me.

I need to live stream/record badminton matches. A little bit of explanation here. Badminton is played indoors and since most of the venues concerned are not exactly well lit (for recording), I would need a good low light camcorder. Now the venues vary in size and depth etc... which means the camcorder sometimes has to be very close to the court and sometimes far away... e.g. as seen below:

Near location.

Far but zoomed in and offset.

As can be seen above, I sometimes maybe need a wide angle lens to accomodate the closer shots but then I also need some height as the shuttlecock (as it is called) can reach quite high above so I prefer it be visible most times.

Above shots were taken with a Canon Vixia HF R800 with normal lens. As I mentioned, live stream is the main method that will be applied so I did use HDMI extenders and Camlink 4k capture device and streamed everything to Youtube using OBS.

Example of live streamed video above here: https://youtu.be/2jMC-9k9nac?t=9929

So my question is several fold:

1. I want to invest in a better (4k) camcorder which would do better in low-light/artificial light conditions (high fps will be of great use in the future with replays and slow-mos.

2. The workstation doing the streaming will very likely not be close to the camcorder so I would need extensions (hdmi extender/sdi?)

3. I would need to capture crowd noise along with the umpire (the person refereeing the match as seen sitting on the high perched chair) and also maybe commentators in the future.

4. In case of bad internet, record the footage to be uploaded later.

I would appreciate if anyone could give me some precious advice on any or all of the above and maybe some other aspect I've not considered.

Thank you loads and I remain at your disposal.