How to check my version of PHP Fusion without logging in ?

That kind of error can occur when MySQL service is not running, or not configured properly. Maybe contact your host with those details and perhaps they can shed light on what's happening, or where the disconnect is.

Do you have phpMyAdmin? If you do, and still can't login, that's more than likely why. To answer your question, The only ways that I would know how to determine your version would be to check the original zip that you downloaded. Usually the file name is associated with the version. Other than that, you would have to login to the administration panel. The top panel title contains the version info. Obviously you can't try that one since you can't launch your page.

The version number is stored in the settings table

You were right, it was host company fault. For some reason I did not have the full name of the database. It should be $ DB_HOST = "sql2.1000gp";
and it was earlier: $ DB_HOST = "SQL2";

Anyway, they changed it for me, website is working fine but I have noticed that BBcodes stopped working now :(

I had to disable all of them.Is there a way to make it work again ?

You have lost one table at least. It is "fusion_errors". If this table does not exist your site will not work when the fusion tries to log an error.

If you have a daily backup, you can restore your system. If you do not have backup, ask your hosting provider if they have. If nobody has backup, install a new fusion using different table prefix, and rename any table in the new installation that does not exist with the original prefix.