Can we use the Page API outside Moodle to create new pages that are related (i.e collect and insert and update) to Moodle database?
Probably not like you're thinking.
The Moodle Page API is concerned with building the HTML of a page - HTML headers & title, adding links to Javascript & CSS files, etc. - rather than being a API for content management.
If you want to create web pages of content, you need the Page resource. Conceivably you could build something to post content to Moodle's new Page resource code, but I'm not sure how easy or reliable that would be.
HTH,
Dave.