Tantalum caps are classified as electrolyte- they tend to be slower (ions rather than electrons form the double layer). Ceramic caps, on the other hand, depend on the dielectric polarisation- they can be much faster- you can figure out that by looking at their frequency limit.
In addition, many ceramic caps shows relatively strong voltage dependence of of capacitance (but the magnitude depends on the material)- the effect is small for electrolytic caps. Both ceramic and electrolytic caps have relatively large margin.
It is the response to the changing voltage that determines the series resistance: it is somewhat virtual in some sense because that also depends on the frequency (and to a smaller extent on the bias voltage).
Yes, you must consider the voltage drop (as suggested in #3) and act appropriately. What is the max freq you are planning to use?