I would like to create File Server, able to read, write, rename, delete or move files through my browser
There are three parts to what you want to do. First, the Arduino needs to be able to read, write, rename, delete, or move files on the SD card, with no interaction with the ethernet shield. Is your Arduino sketch able to perform these functions?
The second part is for the Arduino to serve up a web page, with form, that contains controls to enable the user of the browser to be able to perform the required actions? Do you have a vision of what that form should look like?
The final part is for the Arduino to receive the form back when the submit button is pressed, and to distinguish between an initial page request and a form submission. Do you know how to do that? When you do, invoking the right function (delete(), read(), rename(), etc.) with the correct arguments will be trivial.