It still keeps asking for that fucking root\s password even i open\acces roots console or write that sudo su in the console. I cant install anything if i dont know that password.
All you have to do to "get root" is open up a console (e.g. by clicking on the KConsole icon in the Kicker bar at the bottom of your screen) and typing su. It doesn't ask for a password.

If you need to set a root password, as the regular ("Knoppix") user, all you have to do is type sudo passwd in a console and it will ask you to supply one. (If you're already root, omit "sudo".) After that, you can supply your newly set root password to KDE when it asks.

Note that even after setting the root password, you can still "get root" by typing su in a console. It still won't ask for a password. (Wonder if that behavior continues even after installing Knoppix to hard disk.)