Need to make a separate independent page with all posts (like the main page using in theme). Also need to have the ability to change the view of posts of this page (independently of the main page). How it do?
There are a few ways to do this, some more complex than the others. The simple way is to create menus based upon Post Categories – WPBob has a good tutorial
Alternative I would recommend looking at Tom’s WP Show Posts – awesome plugin that allows you to create custom post pages and place them anywhere using shortcodes