Hello, miyalung.
Thank you for contributing to Apple Support Communities.
We understand that you’re experiencing issue where the Mobile Pixels 12.5” DUEX Plus Lite monitor on your MacBook Air is no longer working and you’ve gone through some pretty extensive troubleshooting, without success.
In reviewing the support site for Mobile Pixels, it looks like they strongly recommend using the USB-C to C ports to connect your monitor. You mentioned you’re using an HDMI cable, and while this isn’t an option shown for setting up your monitor on their Installation Guide, they do mention that for any configurations that are not USB-C to C, you’ll need to download and install their drivers. You might start there:
Installing Duex Plus/Lite – Mobile Pixels
Download Drivers – Mobile Pixels
Quoted from Mobile Pixels:
"If you have Type-C port(with DP signal) on your laptop, driver installation is NOT NECESSARY. We highly recommend you directly connect the monitor(s) with your Type-C port on your laptop for a better experience."
We also wanted to set you up for future success with your MacBook Air. The new Mac computers with an M1 chip function no longer support resetting the SMC or NVRAM.
Cheers.