Should I list on my CV research assistantship positions under grants&awards?
Although merit is certainly a factor in the hiring of research assistants,   most people don't consider assistantships as "grants or awards". They are jobs. List them under "Positions Held" or "Academic Appointments" or the equivalent heading on your CV. Do not list your salary or the amount of your stipend - that's not anybody's business except you and your department.

Some fellowships might be considered awards. They would usually be explicitly competitive in nature, and given by outside agencies. "Named" fellowships from endowed funds might also count, even if awarded by your department. But a research assistantship is not a fellowship.