issue is clear now. On the page and forum there are 4 people - me, my friend, his girl and test account. I have had user and theme intergration turned on. Then, once I wanted to log in into the forum admin panel (I was already logged in to the site and forum with correct nickname, login integration worked fine) - I couldn't. Forum says that i have incorrect password. Impossible! To check this, i logged out from the site, and logged in from the site - username and password was right. But still same problem while trying to get to the forum admin panel. Than I logged out, and tried to log in from the forum - I couldn't - "incorrect password". So the issue was clear - forum accounts was broken.
The same problem had my friend, but! His girl could log in. I clicked the password reset for my accound. No email has come. So I got into the forum profile settings, and then I saw that... I had e-mail of this girl, an everybody had except of testing account! My password reset gone to her e-mail. She gave me the link and the password so that I now can login. This could be all, but...
...I can't change my e-mail back, as it says that this e-mail is already used. I check it in the admin panel - no user have my e-mail. My friend can't change his e-mail back, too. Have you got any idea how can we fix it? I really don't want to create new e-mail accound just for the forum. After this all I turned off the user integration.
Very strange. I wasn't logged as another user. I was logged as me, but with her password and e-mail. I checked it in the WP-United user mapping, and the accounts was connected correctly.
Now about theme integration and login problem: the temple I was using goes that way:
<?php get_header(); ?>
<?php the_content(); ?>
<here was code with the sidebar>
<?php get_footer(); ?>
Visually it worked OK. But I could not log out from the forum main page. On other forum pages i was once logged in, once logged out - changing with page refreshing.
The last thing is that from time to time my site get the MySqul error, while nobody can view it. I don't have the error screenshot nor text, but once it was "error 500". I suspect that this all is about WP-United.
I will post this problem on your forum soon.