What do you think on how often the information is updated in Google? I mean if, for example, website content is updated, how long it can take for changes to start taking effects? For example, I have made a spelling mistake in key phrase for a website and my website began to be displayed in Google under the wrong key phrase! I changed the content and corrected a spelling mistake 1 month ago and as far as I see the change still take no effects.

A few days after the page is re-indexed.

How often changes are implemented really depends on how frequently your website is crawled.
And the crawl frequency is affected by things like how frequently you update your site and how often pages that your links are coming from are crawled

The easiest thing to do is to get a Google webmaster tools account and then you can tell exactly when your pages are crawled

It depends on how often you want search engine bot to visit your page/site. You can set it in your sitemap.xml that is submitted in google webmaster tool.