Is possible to continuously create new posts in a website changing the content daily or to update the content of the existing posts for Google and other search Engines to optimize your website? can this give you a good SERP? Does the number of posts in a website influence the way Search engine display search results for your keyword?

Posting in a website or a forum? Posting positive and contributing content within a do-follow forum does help with your SEO. Also, updating your site regularly with quality content will improve your on-page SEO as well.

ITs not really important if you are talking about blog or forum

I don't this is an issue in case of Blogs and Forum because i have seen many of the users with around 200-300 Posts in an Forum.

basically, fresh content that is unique and relevant on a frequent basis as well as 'quality' back links can help you a lot in the SERP's

The number of posts itself does not count. But as more posts, as more content the website has, so it's better for the search engines. The conclusion: try bringing as much posts as possible.