You need to look into 'FTP'.
The conventional web we browse is based on 'HTTP' is designed for viewing text, images, etc. but not for file transfer. 'FTP' is designed this in mind and if you can access your server using FTP you should be able to do most of the operations that you are trying to achieve.
This class is a wrapper for FTP which is built-in to C#. It should help you. If it doesn't, well, try the code FTP commands and try playing around with them.
Hope this helps, Regards