Can I change SSN status from "not valid for employment" to "valid for work only with DHS authorization"?

you don't get a Social security card as an international student unless you work. As a international student you are only allowed to work on campus. If you get a job on campus you will need to get a new social security card. The one you got as a child is useless, but hold on to it, as they will want to know whether you ever had one and what the number is.