Number 1: If you go to System Manager > Tools > Message Tracking Center you can track message inbound/outbound by adding the necessary info. In your case, the server, and either the sender (your) email address or the Recipients (their) email address. Then click the FIND button.
Number 2: I would look at System manager > Servers > YOUR SERVER NAME > protocols > SMTP > Default SMTP Server. The Access Tab and Delivery tab contain most of the info you need to look at. I would also double check that you are not on any blacklists (just google the term).
Number 3: Same as Number 1