  We characterize the convex-cyclic weighted composition operators
$W_{(u,\psi)}$ and their adjoints on the Fock space in terms of the derivative
powers of $ \psi$ and the location of the eigenvalues of the operators on the
complex plane. Such a description is also equivalent to identifying the
operators or their adjoints for which their invariant closed convex sets are
all invariant subspaces. We further show that the space supports no supercyclic
weighted composition operators with respect to the pointwise convergence
topology and hence with the weak and strong topologies and answers a question
raised by T. Carrol and C. Gilmore in \cite{CC}.
