MacBook Air may be compromised or malfunctioning?

Oh, good- Malwarebytes is fine. In fact, it's exactly how you should scan your Mac for adware/malware/etc. Odd that nothing was returned, but I have a few ideas-

Regarding the popups, it seems like your Keychain Access lock time is set to ask for it every time. Try this-

1. In the Keychain Access app on your Mac, click “login” in the Keychains list.
2. Choose Edit > Change Settings for Keychain “login.”
3. If the "Lock After" checkbox is checked, it'll ask for it after a certain number of minutes. Make sure this is unchecked!
4. Similarly, uncheck the “Lock when sleeping” checkbox. This keeps it from asking for your password every time it locks.
5. Click Save.

As for the sleeping/waking, try these steps-

• Check Activity Monitor to see what processes are taking up the CPU
• Try resetting the SMC (System Management Controller)

These general steps should help with everything-

• Ensure your software is up to date
• Try resetting the NVRAM/PRAM
• Start up in Safe Mode to see if the issue persists
• Reinstall macOS (does not delete data, but backups are wise to have)

If none of that helped, you may need to erase your Mac, then restore it from a backup-

1. Use Disk Utility to erase an Intel-based Mac - Apple Support
2. Restore your Mac from a backup - Apple Support

Hope that helped!

These programs (and any that claim to 'speed up' or 'de-clutter' your Mac) often do so by deleting important system files or doing things to your Mac that they then claim to be able to fix (after you pay them).

Effective defenses against malware and ot… - Apple Community

To turn off U.S. in menu bar go to System Preferences > Keyboard > Input Sources and deselect Show Input menu in menu bar.

This sounds like adware/malware. Have you installed any free "Mac Cleaners" or similar programs?

That's normal behaviour. My Mac shows US when starting and disappears after unlocking, even though my keyboard is set to AU.