NVM

@davidsword – thank you for reply!
I didn’t know about Debugging in WordPress, thanks! The wp-admin works like a charm, and I found the cause of my troubles.

In the page.php just add a condition to checking post (erm, I was confused, because I was sure posts are not the same as pages, but anyway…) and then get a content.

For others:

if ( have_posts() ) while ( have_posts() ) : the_post(); ?>
		<article id="post-<?php the_ID(); ?>">
		<?php if ( ! is_front_page() ) { ?>
			<h2 class="entry-title"></h2>
		<?php } ?>
			<section class="entry-content">
				<?php the_content(); ?>
			</section><!-- .entry-content -->
		</article>
 <?php endwhile; ?>

and now all works fine. I just forgot about the Worpdress loop and wonder why it not works 😀