@gwire
Let me try to answer some of your questions.
1. Start reading from post #1,884 for PS2 information. For logfiles, Samba should be enabled, so you can access the Samba shares from a remote location. E.g from a windows pc you can access the logs via: \\libreelec\Logfiles
A script will automatically run to collect the required logs, and zip it for your. You only need to attach it to your post (no need for pastbin).
Read the info and link in post #1 carefully.
2. There are some tools installed with this build to test controllers, sdl2-jstest and hcitool. (I only used jstest)
/usr/bin/sdl2-jstest -l (look for Joystick Number:, which can be 0)
Dolphin has its own controller configuration, and you need to be aware of the option to toggle maximize/unmaximize a window with [ALT] + [F10]
[Esc] > stop game and go to menu
[F10] > resume game
[ALT] + [F10] > toggle maximize/un-maximize a window
Remove stats on screen:Options > Graphics > Advanced > Show Statics
3. See 1.
4. What do you mean. Do you hear menu-sounds, but would like to switch them off, or are you missing menu-sounds using a controller?
I suspect the last one, as that is what I observe. Don't know, didn't check if there are options to have menu-sounds with a controller.
5. The logs should help to find if the hardware is recognized. See 1. for logs.