Design is what makes the rest of it look like it came from the same company. Motion designers animate — titles, lower thirds, explainers; graphic designers set the things that do not move.
Usually a fixed price per asset or per set, with revisions counted. Animation is priced by the second far more often than people expect, which is why a ten-second title sequence can cost what a much longer edit does.
Bring whatever brand material you already have, even if it is only a logo and a colour you like. Design work done without it is a guess, and the second guess is the one you pay for twice.
You say what you are trying to achieve rather than what to buy. Lucy shapes it into a brief, prices it against what people here actually charge, and shows you the creators who can do it. You agree a figure before anything starts. The money is held until you approve the work, and Lucy takes 15% of the creator’s fee — never a fee from you, and never anything on approved expenses.