Chifu, if the theme editor says that your files are not editable, it is because of the way the permissions are set for the file in the web host itself. I’m a relative newbie, so I can’t recall which numbers are what, but basically if you are able to go into where your files are hosted (the place you initially uploaded them), each file should have a three-digit number connected with it. A 555, 666, 777, or some combination thereof (667, etc.). Those numbers indicate whether the file is readable and/or writable by the owner, the world, etc. You need to “change permissions” in there, to make the file writable, or else WordPress can’t write to the file from your user interface.
I’m not sure who all has to have write access, though – maybe someone more experienced can answer that.