User Password Expiry date is null in user_users? Is it possible to find my password expiry date without asking the DBA? 

My user does not have privileges to view the DBA_USERS table. Also, I tried select * from USER_USERS table, but expiry_date is empty.
It might be that your account has been assigned the profile with PASSWORD_LIFE_TIME set to UNLIMITED, and thus your password will never expire. You can query the USER_PASSWORD_LIMITS view to determine what password limits are currently in effect for your account:

SQL&gt; select * from user_password_limits;

RESOURCE_NAME                    LIMIT
-------------------------------- ---------
FAILED_LOGIN_ATTEMPTS            10
PASSWORD_LIFE_TIME               UNLIMITED
PASSWORD_REUSE_TIME              UNLIMITED
PASSWORD_REUSE_MAX               UNLIMITED
PASSWORD_VERIFY_FUNCTION         NULL
PASSWORD_LOCK_TIME               1
PASSWORD_GRACE_TIME              7