The step where you tested with a new account has shown that your corruption is simply to the user settings and preferences and not some problem with a systematic bug or a conflict between software.
Sadly, you have several programs with corruption according to the screen shot and you may need some time to figure out exactly which settings are causing you grief.
To start - estimate how much time you will need to just move your documents over to the new account and write that estimate down. Also start a full backup to ensure you have a good recovery point.
Then spend one third to one quarter of that time clearing settings, looking to delete preference files/that are related to the affected corruption.
The menu bar icon location is stored in ~/Library/Preferences/com.apple.systemuiserver.plist
So, you can start with these two articles and the step above to see if you want to try and fix each of these issues by re-creating the affected preference files by dragging them to the desktop (or the trash) and rebooting:
Once you've spent some time fixing each item you have noticed breaking, you can check with your original estimate on how long it would have taken to just start moving your documents over and re-choosing your settings. Hopefully, you picked the shorter route to clearing this corruption. The benefit of just starting new is you don't have to notice all the things that are wrong and hunt them down one by one. You will remember you like this desktop picture and that layout and change the things you care about quite easily over time.