MacBook Air and LG Ultrawide Display issues

Anyone else having issues with MacBook Air 2020 cooperating with LG Ultrawide monitors with LG's split screen software not functioning and the MacBook Air not recognizing the actual screen size of the model. Though the display is legible and sharp and appears scale correctly, but I need to be able to split the screen into up the four windows, but the OnScreen Control app is not recognizing the MacBook Air when opened. Ultrawide Monitor is about 3 years old - LG34 UM61-P.

Also, is there any way to just have the monitor window displayed when the MacBook Air is closed without the power cord plugged in all day long? I rarely need to have both the MacBook Retina display and the monitor display opened on my desk a working together at the same time.