I have some difficulties with page.tpl.php
I mean page.tpl.php overrides node pages


That isn't true, I just think you haven't quite understood how templates work in Drupal. The hierarchy for templates is:

html.tpl.php
  page.tpl.php
    Everything else (including node.tpl.php)


So as you can see, node.tpl.php is inside page.tpl.php, it's not a replacement for it, nor does it override it. But since you're not outputting the main content block in that template file, it stands to reason that the page content will be empty. Unless otherwise specified by perprocessing/template suggestions, page.tpl.php will be used for every single page.

You also need to know that everything (including the main content) is a block, which must be put in a region in page.tpl.php to be displayed. You would typically find the main_content block in the content (or similarly named) region.

To fix your problem, you need to add the main content region back into page.tpl.php.