= Solution
Use the momentum-space <Feynman rules> with all momenta conserved at each vertex. The free <scalar propagator>, free <Dirac propagator> and <pseudoscalar Yukawa interaction> vertex are respectively
$$
\boxed{\frac{i}{k^2-\mu^2+i0},\qquad
\frac{i(\not p+m)}{p^2-m^2+i0},\qquad
-i\lambda\gamma^5.}
$$
The <Dirac propagator> follows by multiplying the inverse kinetic matrix $\not p-m$ by $\not p+m$, using the <Clifford algebra> to obtain $(\not p-m)(\not p+m)=(p^2-m^2)I_4$. The vertex follows by expanding $e^{iS_{\mathrm{int}}}$ once: there is no factorial because it has one scalar and two distinct spinor field factors. An internal scalar has no spinor indices; an internal fermion line carries the displayed matrix with its momentum directed along <fermion flow>.
These rules use the coefficient exactly as printed. With the standard Hermitian $\gamma^5=i\gamma^0\gamma^1\gamma^2\gamma^3$, the <Hermiticity of a pseudoscalar Dirac bilinear> gives $(\bar\psi\gamma^5\psi)^\dagger=-\bar\psi\gamma^5\psi$. A Hermitian physical interaction therefore requires $\lambda^*=-\lambda$; writing $\lambda=ig$ with real $g$ changes the vertex to $g\gamma^5$. This convention issue does not alter the formal rules above, and no unstated real-coupling assumption is needed.
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