On working as a freelance copy-editor in graduate school
Who says you're any good at it? Why would a colleague pay you for such a service when many lab-mates or other colleagues would do so for free or a promise to return the favor later? Who says anyone local to your area would pay you for such a service? Freelance implies not working for an existing service, so are you prepared to deal with the necessary tax implications of being self-employed (in the US or your country)?

I wouldn't expect this to appear on a CV, and I would find it strange if I read a CV with it this experience listed unless the candidate worked for a professional editing service (where it might be a plus for them).