The dynamic model is
$B(q)\ddot{q}+S(q,\dot{q})\dot{q}=\tau+\tau_k$
Where $B(q)$ is the inertia matrix, $S(q,\dot{q})\dot{q}$ are the centrifugal and Coriolis terms, $\tau$ is the actuator input and $\tau_k=J^T(q)F$ is the torque imposed by the external force.
So since at rest $\ddot{p}=J(q)\ddot{q}$, $S(q,\dot{q})\dot{q}=0$ and we have no actuator input, substituting $\ddot{q}$ from the dynamic model we have
$\ddot{p}=J(q)B^{-1}(q)J^T(q)F$
I assume that for the point 1, for the second principle of the dynamics, the end-effector accelerates as in the case B. Now, in the point 3, if we have non-uniform masses of the links, the second principle of the dynamics is still valid? I guess I can choose an inertia matrix $B(q)$ with proper centers of mass of the three links such that at the rest configuration $q_{eq}$
$\ddot{p}=J(q_{eq})B^{-1}(q_{eq})J^T(q_{eq})F=\begin{bmatrix} p_1 \\ 0 \\ 0\end{bmatrix}$
and so the end effector accelerates as the case D right?