However nobody knows why Google makes Sitelinks for some websites ans why it doesn't make for others, i guess some parameters are important for having Sitelinks in Google and they are Pagerank and traffic.
I want to know other parameters that you know to have Sitelinks in Google?

Google does not give sitelinks for every site. They give sitelinks to reputed sites only. Also site design effects whether Google able to create sitelinks or not.

http://www.webmaster-talk.com/the-go...e-results.html

enough discussions there to keep you going.

And the answer to why? Is Links and anchor text.

Is it true that when doing a search on Google, priority sites featured also receive additional links underneath them directing users to core areas of the site? Can these links be collated if our site is displaying old links? Is it possible in any way to influence this listing in order to manipulate the link building process? I would really appreciate any help in this matter, as I really am in a hurry to create a better link structure for my site. Does anybody have experience in this matter? Can somebody help me?

The forum search works quite well

Google Sitelinks

If you are talking about Google sitelink (As given in webmaster tool) then It will not be counted as backlink to your site.

These are the link which Google consider important on you site. Recently One of my blog is started showing backlink (total 8 links) below my site meta tag in search result and I found that these are the link which maximum visitor clicks on my site.

Oh wow. Didn't know it was part of their system and only certain sites get it. Is it free?

Originally Posted by vWiz

Oh wow. Didn't know it was part of their system and only certain sites get it. Is it free?

It is not any product or services which you can buy.
It is Google who decide whom to give this stuffs. You just work hard on your site and in future you will get it also...(but not guaranteed)

Site Links are not guaranteed. Search Engines Provide site links to make user experiences better.

One can't assure you site links but they come as traffic on the site increases.