Yes, you can!

Setting up UI under WSL is a bit of a pain, because there's nothing out of the box - so you need to set up X on Windows, or use VNC or RDP. RDP is the easiest by far right now - just install xrdp in WSL, edit the config so that it uses a different port, and connect to localhost from Windows. The result looks like this:

https://i.imgur.com/DSmLjUM.png

It's not really supported, but you can run GUI programs with some amount of success by setting up X forwarding. Some programs work better than others, but I probably wouldn't want to run my code editor in it.

No idea. I've only ever tried running cli tools and programming run-times.

with X server