Yes, you should have a noun, pronoun, or a noun phrase after "regardless of".
Your usage of it in (1) and (2) looks fine, but I think (3) is a little odd.
In (1) and (2), you're saying the person will continue on no matter what happens, meaning the outcome is of no concern.
In (3), it's saying a certain fact holds true in both of the two areas mentioned, and so the two things strengthen the point by being relevant rather than "of no regard" (i.e. regardless) . In this case, I would use "whether it be/is your job or study", or "in both your job and study".