Material

It is best to modify the material using the "Component Material" panel below the tree. The items in the tree are mapped to the fields on the panel. Because there is only one panel and multiple Material records in the tree, you must select an item of a component, to display its material in the panel.

The panel provides a bit of contextual help - hit F1 when a field is active for a short explanation of its meaning, or click the "arrow with question mark" toolbar button and then click on a field.

To answer your questions, A is alpha channel, but you must explicitly enable transparency at the bottom of the material panel (because texture may have alpha channel as well and you must choose which one to use).
Specular defines the color of reflected light and the fourth number is the sharpness of the reflections.
Reflection is color of a mirror-like reflection (this is only visible when using the raytracer, the interactive OpenGL renderer cannot render mirrors).
(If you set all fileds to 0 and Reflections to 1,1,1, you'll have a perfect mirror.)
Refraction indices ratio is the ratio between the refraction index of the outside and inside materials. It is hard to explain without some background in optics. In short, you can use it to create lens-like effects. The material must be semitransparent and the direction of the light ray is modified depending on the angle between the ray and the normal vector of the surface. This effect (lik mirrors) is also not visible in the interactive renderer.