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What you're saying is mostly correct, but your language is a bit imprecise, which makes me think your understanding is a bit incorrect. To be clear: there are both static electric fields, as well as time varying electric fields, which occur together with magnetic fields electromagnetic (EM) waves. The equations you're using describe reflection and ...

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The last part is possibly the most interesting in that you have think about what happens to a dielectric when it is placed in an external electric field, or put another way; how does the movement of charges within the dielectric change the net electric field between the plates?

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You have the right equation. Since you are not given absolute values, you should just reference your answers to the original $Q$. For example, you can say for the first part "The charge will be 0 when the voltage difference is 0. As the voltage difference increases to $\Delta V$, the charge will increase (proportionally) to $Q$". No numbers were needed... ...

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Probably, surface induced charge density has been a' priori excluded by the author while replacing rho=divergence of polarization vector, because this relationship could be established if we consider rho=volume charge density only, and no surface charge density. This result emerges if we try to find the electrostatic potential at an external field coordinate ...

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Dielectrics are electrically neutral as they have no free electrons, which would otherwise make them a conductor. So the total charge should be zero with the surface and volume bound charges cancelling. When it says: $Q_T = f(\epsilon_r,q)$ does the $q$ perhaps stand for the charge and is a more general expression applicable for non-dielectrics?

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