If you move an asset out of a folder it will create a redirect with the same name as the asset you moved out. So you cannot move it back because there is already a file with that name in it.
You could try to make a brand new project. Then migrate all your content into this project and abandon the other one. Do a fix redirect before you migrate.
I had that weird problem of autosave files need to be resaved when deleting, or moving assets, or fixing redirect. But other than that everything seems to be the same as with UE4. So maybe there is something wrong with your folder permissions. Also as someone mentioned already: Make sure you’re project isn’t open twice or an old Unreal service is still running on your machine that keeps you from saving.