A quick check with Google Maps shows that the 11 and 16 bus lines run near Chautauqua Court into downtown. The 28X Airport Express runs from downtown to the airport. There are also private bus lines that provide airport service as well. As Blair suggests, you should check the Port Authority web site at http://www.portauthority.org for current schedules.
As to crime statistics, visit http://www.city.pittsburgh.pa.us/police/html/crime_stats.html for instructions on searching for statistics.