  We prove existence, uniqueness and Lipschitz dependence on the initial datum
for mild solutions of stochastic partial differential equations with Lipschitz
coefficients driven by Wiener and Poisson noise. Under additional assumptions,
we prove Gateaux and Frechet differentiability of solutions with respect to the
initial datum. As an application, we obtain gradient estimates for the
resolvent associated to the mild solution. Finally, we prove the strong Feller
property of the associated semigroup.
