If a member has Private Messages enabled, AND they have it enabled to send their registered email a notification of that PM, then their email will receive a notification. Otherwise, the user will see the PM when next logged in to this site.
If the member has email messages enabled, they will receive a notification to their registered email address of the message.
As far as your other questions... you should be able to click on any user's name and view their profile. Or, I am not following your line of query.