Yes, you can. After the password reset, you can logon with your new password immediately and continue working.
No, the MyPassword site only stores the questions and answers.
No, by default the MyPassword site encrypts the answers to your security questions.
Yes, it is possible to reset a password that is expired using the MyPassword site.
No, it is not possible to reset your password if your account is disabled, or unblock your account using this site.