I’ve implemented a spot light and placed it under big plate (1).

[attachment=30140:Shadow Question.gif]

On top of the plate I’ve placed two smaller plates: (2) and (3) with a little space between them.

There are 2 problems:
a. My shader calculates color for plate (2) as it is not occluded by plate (1).
b. Bottom of a plate (3) is rendered much brighter than it should be.

It seems for me that the only way I have, is to implement shadows to remove these artifacts.
Question1: is it correct?

I’ve read that there are several different ways to implement shadow effects:

1. Via shadow mapping.
2. SSAO
3. SSDO (improved SSAO?)

I have an idea that Shadow maps should be used with SSAO/SSDO to make final image better.
Question2: is it correct?

SSAO or SSDO alone will not completely fix artifacts (a) and (b) on the picture.
Question3: is this correct?

For now, I am thinking on some simplest shadow algorithm implementation and after a while replace it with more advanced.
Question4: which algorithm would you suggest?

Thanks in advance.
PS: I am using real-time rendering.

Also, while choosing a shadowing algorithm, keep in mind that different algorithms are better suited for different situations. For instance, in a large outdoor area with a single directional light (e.g. the Sun), many use cascaded shadow maps, while indoors for instance variance shadow maps.