You're right in that it is just like having another computer. You'll have to download any packages/libraries that your web site needs, unless they are bundled in the bin directory of the site when you deploy.
To transfer files, you shouldn't use ftp. Instead check the option "local drives" under "local resources" when setting up the remotde desktop connection. When you're connected, that will give you access to your local files so that you can copy files between your local machine and the server.
