I’ll use in this week Security in different computers. This computers aren’t mine so I don’t know if they contain or not a keylogger. Then I whant to log in with a different password than others sites of Stack.
Is it possible?
Have you considered not logging in this week and acting as an unregistered user? Or creating a new account using a different email?
To answer your question though, you have an ID, whether OpenID, SE etc that is your SE-wide presence. So it will be one password.
What I don't understand is your threat model - why do you need different passwords on SE sites? What are you protecting against?