Can't use loop cut on some faces I can't describe it with words, so I recorded video.

video

And I can't even cut them separately.

Can anyone help with it?
So as I said you have inner faces, but there are hidden so you need to unhide and delete. You can't create edge loops if the edge separates more than 2 faces, and by the way those inner faces are not good for your topology, it may create artifacts.