Is there a way for you to connect ot the Fedora server remotely? If you know what telnet is (and I don't say that to insult your intelligence, but just to start with something), SSH is similar, except more secure. If you know about telnet, then what you'll want to do is find out if your hosting company permits you to connect to the the web server via telnet or SSH. If you've never used SSH, you will need to download a client. The most common one is probably putty and it can work on Windows. Just do a Google search for putty or putty.exe and several links should turn up.
I know this sounds like a lot more information that has nothing to do with your problem, but as you work with Linux more, you eventuall come into situations where you can't differentiate between problems with the OS or with PHP, such as your problem with mkdir and chmod.
My guess is that the user account that the hosting company gave you limits your use of chmod. You may want to ask them just to be sure. Sorry if I've confused you with my responses. Just trying to help. If you have no way into the server, you probably just want to call their tech support and explain what you're trying to do. Hope this helped.