A) The mail you send is sent using a smtp server running on your own computer. Be aware that many mail servers do not like getting mail from computers that have no MX record, as this is usually spam.
B) You will only be able to read the mail recieved on your own smtp server. I.E. you can't use the mail command to get your Hotmail mail. Mail is read from /var/spool/mail/<you>. To recieve mail, the mail must be sent to firstname.lastname@example.org