Mixed topologies on Saks spaces of vector-valued functions

We study Saks spaces of functions with values in a normed space and the associated mixed topologies. We are interested in properties of such Saks spaces and mixed topologies which are relevant for applications in the theory of bi-continuous semigroups. In particular, we are interested if such Saks spaces are complete, semi-Montel, C-sequential or a (strong) Mackey space with respect to the mixed topology. Further, we consider the question whether the mixed and the submixed topology coincide on such Saks spaces and seek for explicit systems of seminorms that generate the mixed topology.
Comment: Some of the results of the former version arXiv:2207.04681v1 of this paper are now contained in: arXiv:2307.09167 and arXiv:2307.16299