The only vertex allowed in the diagram has two fermion lines connected to a photon line (a continuous fermion line must be drawn, but for discussion purposes, the segments on either side of the vertex points constitute separate lines). See for example Figure 1.7 of the text.
The 17 diagrams contain a loop. The diagrams must be topologically distinct.
Follow the hint I e-mailed on Sunday.
The speed of sound in a gas depends on the density ρ and pressure P of the gas. From dimensional analysis alone we can determine that the dependence must be of the form
Similarly, the speed of a wave on a string can depend on just the tension in the string T and the mass per unit length λ. From dimensional analysis we can determine that the speed of a wave must be proportional to the square root of T/λ.