@Blomman It is pretty typical of official RW support to give a very general response to a first email. And to be fair, it probably sounded initially like the problem may be with Rapidcart Pro. But when you have publishing problems it’s definitely a RW “thing”. Simply go back to RW with this more detailed information. Then they can give you some pointers on how to sort things out. @Aaron: I’ve tagged you so you can maybe help Anders offline.
If you are getting a warning about index.php and index.html files in the same folder then take that seriously. It means what it says. You are just blowing off good info.
So it seems you have 2 problems: one with publishing, one with deleting the extra index file in certain folders (you probably want PHP and not HTML but I’m not sure).
I can’t help at all with the publishing. But if you have an FTP app (Cyberduck, Transmit) then go into your server and check out relevant folders. You will indeed find an index.php and a index.html in some of them. (Which ones: I have no idea!) Delete the one you don’t want. (Which one? I have no idea, but it’s probably the PHP one you want.)