Yes, all settings are correct. Nothing changes except the skin (also some "Run script:" shortcuts become blank in administrator mode). And next time you open Mediamonkey (with or without administrator mode) your skin doesn't come back. You'll have to manually select your skin.

Running as administrator doesn't use a different user account, though that function does exist and has a similar name. It is necessary if you want MM to maintain file associations.

It is possible that the MediaMonkey.ini file has somehow come to require admin permission to read, in which case MM without admin rights might either fall back on default settings or create another MediaMonkey.ini in a folder with write permission. This scenario is unlikely but it's the only explanation I can think of.

When you run as administrator and MM opens with the Metro skin, are your database and settings all intact and correct? And does MM run Metro skin every time you run as administrator?

You can't install add-ons for all users without running MM as administrator, as they are being installed in Program Files MM folder.

Maybe the real question is why are you running as administrator? Most windows programs do not run as administrator unless specifically told to do so. You don't gain anything from it in the case of MMW that I know of

Yes, I also think it's a poorly named Windows function, but here it is.

Running as administrator:
Right click mediamonkey executable -> click "Run as administrator" from context menu

Explain? Running as Administrator is as a different User thus it uses different settings (default if none were set yet).

If you run MM as administrator, it reverts MM skin to the default Metro skin.