1.Do i need to have a fixed IP address for the Eternet shield?
No. You need one for the router that the Arduino with Ethernet shield is connected to. Your Arduino with Ethernet shield is local on that network, and the router (the internet facing device) needs to forward requests, for the port that the Arduino is listening to, to the Arduino.
2.I have known that Arudino can be controlled by sending orders through internet,
but how can i make a website-looking thingy which has buttons to control the Arduino?
If you have to ask, I'd guess that the answer is that you can't.
There is nothing different in the HTML code that the Arduino serves up. It is generally a simple form with submit buttons whose action is to call the Arduino again. Google HTML Forms.