Cutkofsky cutting rules questions 
Consider the two photon exchange diagrams above. The Cutkofsky rules tell us that the imaginary part of each of these diagrams can be obtained by cutting through the graphs in all possible ways such that the cut particles can be simultaneously put on-shell. I am trying to disambiguate what is and is not an allowed cut.
I am working through a textbook (Forshaw and Ross: QCD and the Pomeron) and when they cut through the first graph they only place the cut vertically passing through the two fermions. Furthermore, they claim that the second graph does not contain an imaginary part. My questions are
(1) What about cuts which pass through only a single fermion? Can we terminate a cut line halfway through a graph?
(2) What about cuts passing through a fermion and a photon?
(3) Can I cut horizontally through both photons in the first graph?
(4) In the second graph, I can draw a line which only passes through the two fermions and not the gluons. Is this a legitimate cut?
(5) Is it obvious that the second graph does not contain an imaginary part?
 A: (1) One cannot terminate a cut halfway through a graph. This is because a cut is supposed to separate a graph into two regions---one where energy is flowing out and the other where energy is flowing in. Cutting through a single fermion is not a legitimate cut. 
(2) Cuts through a single fermion and a photon vanishes as it will contain the eikonal vertex

which vanishes as
\begin{equation}
\int \frac{d^dk}{(2\pi)^d}\delta(k^2)\delta((p-k)^2-m^2)=\int \frac{d^dk}{(2\pi)^d}\delta(k^2)\delta(2p\cdot k)=0
\end{equation}
or more simply put, vanishes because of energy momentum conservation for onshell particles.
(3) Cutting horizontally produces a double photon emission graph which vanishes for the same reason as above.
(4) A cut must always seperate two regions of a graph. The cut which only passes through the two fermions and none of the intermediate photons is not a legitmate cut.
(5) Any cut of this graph will contain an eikonal vertex which, by the above, vanishes. Some of these cuts also contain disconnected graphs, I am unsure if this would be a second reason for their vanishing, as the S-matrix only contains connected graphs.
To anyone who wants to understand the Cutkofsky rules, I highly recommend Veltman's book Diagrammatica.
