Yes, easily. Most OSes let you do that.

Sure, it's part of windows settings under power management.

Yes, in most OSes it’s just a setting you can toggle. But even if you can, you may want to leave it open for cooling. Lots of laptops are barely cooled enough to support themselves, and will often rely on radiating heat out of the case as a form of passive cooling. And even when the screen is open, they still struggle to stay cool. Closing the lid often makes these cooling issues much worse.

Yes usually it's the OS that handles it and it can be set to ignore the lid detection.

I did it for a while. Also removed the battery so it doesn't start swelling