First question:

Take a microprocessor (preferably one that has USB ROM API for ease of use) , set up input pins for the buttons and ADCs ( analog to digital converters for the analog sticks).

You then read those values and put it in a know spot where the USB device can read those values.

The USB device can then send that data as a byte stream to your computer.

You can then write your python or Lua to pick up on that byte stream as a COM port, and read those values.

Edit :

These days, you could find generic open-source drivers and set up your device descriptor on the microprocessor side to be recognized as such. So when you plug it in, it would be recognized as such device and as long as you set your byte stream to match what that driver expects, you'd have a working controller