How often i should re-build and re-submit xml sitemap for news website?
Depending on your server configuration you can setup your site to run cron more often.

You can also use Rules module, To write a rule for resubmitting site map  which can be trigger after certain time or on new content published.

It is also important to mention that search engines takes time to index - no matter whether through external links, internal links or sitemaps.

So don't think submitting site map more often will help.