I tackled a couple of these, hopefully another RadReffer will have a good idea how to find the stats I couldn't.

Murder Rate
The most recent I could find was 2006 with 406 murders from the Philadelphia Police Dept.
2001-2006: http://www.ppdonline.org/hq_statistics.php
Homeless
This article estimates about 261 from Spring 2008. I couldn't find anything solid from a government resource that was city specific, mainly just county statistics.
http://www.kyw1060.com/pages/2697197.php?
Median Income
Again, I couldn't find statistics for this by city, but the FannieMae/HUD website was searchable by city though it then defaulted for county. $74, 300 is what they say, though that seems high to me.
https://www.efanniemae.com/sf/refmaterials/hudmedinc/hudincomeresults.jsp?STATE=PA&choice=msa&CITY=Philadelphia&FormsButton1=Search

Hope this helps!

-Natalie