Please read my article over How to make a Website from WordPress first.
My issue was related to relative path and absolute path, which I came to know later on (Sometime just defining the problem in current copy book terms make the problem half solved). All of the URLs of the same site were seemed to hard coded to be consisting of local IP of the same site, which was an issue, if I was planning to put the same over some public IP for being accessed from outside (as currently we are not planning to own some domain name or web hosting service, so only public IP based access was sufficient).
After exercising a number of options, finally the trick came out to be a simple one. I was to update option_value entry in wp-options table of WordPress MySQL database, where siteurl was mentioned as http://%5BMY_LOCAL_IP%5D/wordpress while it was needed to be /wordpress
I know its kind of stupid, but I am not that into Website deployment or could say missed the basics completely. But anyway, all is resolved now. In next, I was to convert all my manual entered links in the same format. I will keep the same thing in my mind for future reference.
In the next step, I am about to put the latest version of the same theme for the run. Have to check first that how many settings its gonna to change and how much manual work it will require after updating. Wish me Good Luck!