What does vertical axis labeled "events/energy" mean in histogram? 
What does vertical axis labeled "events/energy" mean in histogram? 
Why is events divided by energy 0.1 GeV ?
Why is events divided by energy 0.5 GeV ?   
 A: The events have been binned in $0.5$ GeV groups i.e. we count the number of events with energies in the range $E$ to $E+0.5$GeV, then graph this count against the energy $E$. That's why the units on the $y$ axis are events per $0.5$ GeV.
In this particular graph the count has been normalised i.e. the $y$ axis shows the number of counts in each bin divided by the total number of counts.
A: In general, the total events for these types of histograms are obtained as $\sum_{i\in Bins} \left(\frac{\text{Events}}{x}\right)_i\Delta_\text{Bin}$. In the case of the first histogram, $x=0.5\text{GeV}$ and $\Delta_\text{Bin}=0.2\text{GeV}$. In the case of the second histogram, the two factors cancel out. In some histograms, $\Delta_\text{Bin}$ varies for each bin (it should technically be $\Delta_\text{Bin}^i$). 
The main idea is that the $y$ axis is supposed to represent a discretized $\frac{d\text{Events}}{dE}$ integrand. They are approximating
$\int dE \frac{d\text{Events}}{dE}\rightarrow \sum_{i\in Bins} \left(\frac{\text{Events}}{x}\right)_i\Delta_\text{Bin}$. 
