Multivalued linear operators, also known as linear relations, are studied on a specific class of weighted, composition transforms on Fock space. Basic properties of this class of linear relations, such as closed graph, boundedness, complex symmetry, real symmetry, or isometry are characterized in simple algebraic terms, involving their symbols.

We study certain dynamical systems which leave invariant an indefinite quadratic form via semigroups or evolution families of complex symmetric Hilbert space operators. In the setting of bounded operators we show that a $\mathcal{C}$-selfadjoint operator generates a contraction $C_0$-semigroup if and only if it is dissipative. In addition, we examine the abstract Cauchy problem for nonautonomous linear differential equations possessing a complex symmetry. In the unbounded operator framework we isolate the class of \emph{complex symmetric, unbounded semigroups} and investigate Stone-type theorems adapted to them. On Fock space realization, we characterize all $\mathcal{C}$-selfadjoint, unbounded weighted composition semigroups. As a byproduct we prove that the generator of a $\mathcal{C}$-selfadjoint, unbounded semigroup is not necessarily $\mathcal{C}$-selfadjoint.