can I handle session state load balancing with Big-Ip?? (If yes, which version?) Thanks

F5 has various modules that should be able to satisfy your requirements. I would look at the ASM and APM modules for web application firewalling and pre-authentication respectively, and the LTM module for load balancing and session state load balancing.

Then I would contact a F5 sales person to start the process of getting a solution created to resolve your requirements.