Gaming

I have the Bluetooth + 2.4G one with hall effect sensors and paddles (with the 2.4G/Bluetooth switch on the back and included 2.4G receiver in the dock).

I didn't realise the dedicated 2.4G one received Bluetooth later, but the firmware was for the 2.4G receiver, not the controller, which I'd assume to be the same one regardless? That said, it'd only allow you to use "Switch Pro Mode" and "Xinput Mode" when connected via 2.4G to the receiver. Bluetooth mode behaviour will be unchanged... But given the choice I'm not sure why anyone on PC would use Bluetooth instead of the 2.4G anyway, unless they're not using the dock with that particular computer...

All that aside though, my initial comment was to indicate 8bitdo were actually quite helpful when I reached out to them, in contrast to the person I was replying to... To answer OPs actual questions:

1. Bluetooth mode outputs as a Switch Pro controller by default, so a lot of games on PC won't recognise it unless you use Steam Input or some other translation layer to convert to Xinput. There are numerous applications to do it, but Steam is probably easiest and most accessible. To set the paddles etc You can download the Ultimate Software on your Phone or the PC to set the back paddles and tweak settings.

2. I'd recommend playing around with some first person shooters using the Gyro. Steam specifically has a Flick Stick-like mode that is a really fun way of using the Gyro in FPS games like DOOM. You angle the stick to the direction you want to face, and then use gyro to aim up/down and make fine corrections. E.g. to snap turn 180degrees, just flick the right analogue stick down. Works brilliantly when you (eventually) get the hang of it, it's so much faster.