Answer
a) No.
b) No.
Work Step by Step
a) We know that the change in the potential energy of a system is given by
$$\Delta U=-W$$
where the work $W$ is given by $W=Fd$ where $F$ is assumed to be a conservative force.
$$\Delta U=-Fd$$
If $F=0$, then the change in potential energy of the system is zero, but it can still have some potential energy.
So, the answer is no, the potential energy
could be a nonzero value.
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b) According to the same equation above,
$$\Delta U=U_f-U_i=-Fd$$
when $U_f=0$ at some point that does not means that the force exerted on the object is zero.
So, the answer is no, the force could be a nonzero value.
