how i check my site improvement from seo point according to visitors or backlinks or page rank or alexa rank what i check ?
Get firefox and then download this plugin https://addons.mozilla.org/en-US/firefox/addon/3036/ . It's a really easy way to analyze your backlinks and stuff. Also go to w3c.org and make sure your site is valid HTML and then you can run an SEO report using THIS http://www.iis.net/download/SEOToolkit oops.. I just told you a $500 secret.
Except the 4th one all the other things that you mentioned are really important. Backlinks and Page rank helps you in indexing your site in Search Engines. And visitors are most important from popularity point of view. Try to convince your visitors with their expectations and make them to stay in your site as long as they can. Then checking about your site improvement, first analyze your competitors and see what keywords they are targeting and try to beat them for those competitors by doing proper SEO. Here is a free SEO service which i am using for about an year and i am really comfortable with them.
In my opinion these are the most important factors acc. to SEO for any site. First you have to check your ON-Page of site. Then your keywords ranking and Quality Traffic on your site Backlinks in Google
First check out your ranking in search engines. Set up a Google analytics and webmaster account to get real facts about your traffic. These tools are great. All the important information related to your site's on page and internet traffic are displayed there. So you can get basic idea of your site's performance on Internet.
The increase in visitors. The increase in ranking. The increase in conversions/sales. PR & Alexa is of no consequence.
Check your website ranking, and you can use seo tool for check site backlinks, index pages, etc for site improvement.