MacDonald, Klick, Grunwald:

I never read the paper, but here is my take after quickly skimming it.
They rely on geographic boundaries to identify the effect of police. There is a patrol boundary where UPenn police operate. The idea is that the demographics and characteristics of blocks just inside and just outside this boundary are identical (both are largely students and faculty I think).

The block within the boundary has more police presence (UPenn and Philly PD) while the block outside has less (just Philly PD). I think it said there are double the police inside this boundary line.
The results show are large reduction in crime in the region that has the larger police numbers.



First link (Levitt):

Not sure what you talking about RE: Firefighters. But this one kind of tries to do the same thing as the UPenn paper.
This one is saying that leading up to elections, the size of police force tends to rise (presumably to make the incumbent look better). The idea is that there is nothing special regarding crime in these election years (i.e. election year and previous year are essentially the same).
They also take in account increased social spending and economic conditions in the election years to make sure that that is not driving their findings

Again, they find a reduction in violent crime associated with these increases in the size of the police force