it is more common to say "take a course" (after you have enrolled in it). Improve your skills, practice your skills are better. Revise usually means to change or make a correction.

Sometimes I say "do a course". I'm more likely to say "take a course". I've heard the phrase "revise your skills", but I don't often use it. I'd be more likely to use 'revise' for something more specific. Examples: I need to revise this essay. I want you to revise this assignment. For skills, I'd likely say, 'refresh your skills'. Example: Maybe you forgot many things during summer vacation. You'll need to refresh your skills.

Do you use "do a ... course" meaning study/ enroll in a... course" often? It is normal. Do you say revise your skills? Can do, but no. I just revise. Unless you want to be specific about what you are revising.