liveperson dot com. I think I want to get a unencrypted scripts and modify it so that it would function like liveperson dot com. I was thinking about using a dating site script for example such as vldpersonals. What do you think? Or is there any open source platform to create this kind of features in economical and stable manner? I know the question is a bit vast but wanted to hear your opinions.
Hi shinyyellowstone, and welcome to SitePoint! 
That site looks pretty standard to me, from a glance. What specific features of http://www.liveperson.com/ are you after? Many nice features of websites these days are performed by free JavaScript plugins.