Very likly(but you not informed) your asterisk installation is after NAT.
IF so, you have configure asterisk as described in http://www.voip-info.org/wiki/index.php?page_id=410
Also may need change ports on router/disable SIP ALG on router etc.
Logging(you mean cdr,right?) is controled by /etc/asterisk/cdr.conf
Most likly you have ananswered=no in that file.