why google and other search engines use GET parameters to pass keywords in their URL, when it is possible to track those information into server logs.
Do you mean your server logs ? you can get those information from your server logs. it is best best way get to the analysis of your data. But it is not easy as well.
GET is good for them as it gives the users a chance to save the search url so they can go to it directly in the future if they need
because use GET is most compatible way for all browsers and platforms. It's not dangerous with IP, server side session and client side cookie
Why not? Google and other SE will use simple commands for faster response and process time which are essential in providing information and results.