I am not aware of text-book versions of definition or description of computational science but here are my two-cents based on my experience:
Computational science involves dealing with computational processes. One of the crucial process is programming. So, yes, it involves programming. It is a different issue wether the computational scientist is a writer of a program or not but she will most likely be the user of programs written for specific scientific domains. And it is increasingly likely that she will have to write "glue" code to make things suited to her needs. Hope this answers your first question.
I am not aware of computational material science but assume it is one branch of science which has computational needs, e.g. for simulations of energy and interactions between elements etc. So, yes, it will involve same general principles of computational science like other scientific domains: algorithms, procedures, glue-codes, file manipulation, configuration, visualization and so on. Hope this is close to answering your second question.
The computer science background of yours should definitely help. Wether it is in the scope or not is a bit subjective. However, I would say, it should be very much in your comfort zone given the subjects you have studied.