I have disabled
PermitRootLogin and I cannot login to server by
root, but password is asked from user:
Is this correct? Or there is something here that I'm missing? Why password is asked when it is not permitted?!
The one of the rules of security is not to tell attacker if something is enabled/disabled. This is just one example. The other is logging in as non-existing user. It will also ask for password.
Telling attacker "root is disabled" or "the user does not exists" gives him some information, which you would not want to give away. These are side channels that would allow to eliminate one place of attack surface and focus on some others.
If you don't want to ask for password, you would need to disable password authentication completely.