How would frequent content updation in website helps in searching crawling and indexing rate?

Should we update once in a day or week or monthly?

Would be looking for some valuable suggestions.....

Don't worry so much about crawling frequency -- focus on quality and relevancy to your business or website purpose.
If frequent updates to your content is relevant, then do it. If your content is "evergreen", don't do artificial things to update it.
You do want to keep your site from being "stale", so by all means update and add content on a regular basis, but monthly is fine for that.
Again, focus on good quality content (with your keywords), and inbound linking, and crawling frequency will take care of itself.

That is really helpful tip.. but now a days we are facing too much content duplication and we had came across few of our competitors
are copying our content. In this case if i update my site with quality content monthly than how search engine will treat our content ?

Search engines are always in a search a new and interesting stuffs. If you update your site contents with some interesting and unique stuff engines will surely appreciate that and will be give benefit of it.
You can update the page contents once a week.

Once in a week page updation I think will work, I will try this stuffs for some time .. Is their any third party sites where we can get the backlinks to our inner pages??