How to Recover a gone OSX (mavericks) on MacBookPro?
Problem has been solved, Just thought it may be useful for others.  

1. Is there anyway to get my previous OS to work (I need my passwords and Data in Desktop,documents and download folders)?   


  Maybe, But I don't know yet. But anyway, it is better to clean install
  the OS again to make your computer faster.


2. Even if 1 is not possible, how can I backup the Data of that partition i.e,Macintosh HD? 


  Yes, basically I installed mavericks on a USB thumb drive. Next I log
  in my new OS and copied everything I needed to a external Hard drive.
  Then I formatted the whole MAC HDD and then clean installed the OS
  there. Now it is working well.


3. Is it possible to extract my saved passwords on Firefox as well? 


  Yes, Once I installed the Mavericks on a thumb drive, I went to user
  folder, library/application support and then found Firefox folder and
  copied my profile . After I inistalled the OS on MAC HDD, I installed
  firefox and then pasted that profile in the same place. All of my
  passwords and bookmarks are there.