I'm not a car guy, OK?

F

A bit of WD 40 no? Or the world’s longest wrench

The rim is ruined, the lug nut and stud are ruined. Take the other four lug nuts off [looks like you have done that]. Put the bad lug nut at the bottom after you jack up that wheel. Take a hold of the rim/tire at the top and pull outward hard. Really jerk it and you will break the stud off. You then have to replace the stud of course but at least the wheel is off. Hope that helps.

Applying heat too. A grinder will cut it off. Gonna cut the hell out of your rim. Try using a blow torch and a socket that fits tight

There’s nothing wrong with the nut. The person doesn’t have their car up on a jack.........