I am using WP's own commenting system, but I also want to add option like checkbox which will provide option to post comment on Facebook may be with post link. Has anyone done something like this or can someone point me in right direction? I searched google but there are plugins to completely replace WP comment system I don't want to do that.
you could us "disqus" which does change the wp comments but adds the possibility to use different social media logins to comment. There is also a premium plugin, to be found here: http://premium.wpmudev.org/project/ultimate-facebook/ which might be the better choice if you absolutely need to stick to the built in comment system.