How does the resistance of a photovoltaic module behave?

How does the resistance theoretically behave for most commercially available photovoltaic modules, when an external DC voltage is applied to them, with and without illumination? It's common to wire solar panels of the same voltage in parallel, in order to provide greater current or greater resilience to partial shade.

Do per-panel diodes draw a lot of reverse current?

Individual per-panel diodes are usually added either in single or parallel use so this is not usually an issue. A panel with almost no illumination (= dark) will draw very little reverse current when eg used to charge a battery - voltage wise the same as the parallel panel situation.

Do solar panels have resistance if not illuminated?

Presumably, it can be inferred from this that solar panels consistently have considerable resistance (relative to their rated voltage) when not illuminated— otherwise, having different light intensities on the parallel modules would cause significant current and waste heat to go through the panels at a lower voltage. Is this correct?

What happens if you apply a voltage to a shaded panel?

If you apply a voltage to the shaded panel it will be driven up its load curve to a point where it makes less current at the applied voltage so no reverse current will occur - it will simply provide ABOUT the proportion of full current that the most shaded cell can make. Current output is very close to linear with insolation.