I haven't actually tried to make anyone my sub who didn't already have the Submissive inclination, so I can't really answer that unfortunately. If you want someone as a sub and they're not Submissive you could always enable cheats and GIVE THEM the submissive inclination though.
A Dom/Sub relationship IS a romantic relationship, just with added mechanics. So if you're in a monogamous relationship (with a boyfriend/girlfriend or open partner) you can't also have a sub. But if you have the polyamorous inclination you can have as many poly partners and doms/subs as you want. You get the polyamorous inclination by starting with it, completing the Best Friend questline and choosing to be poly with them, or by cheating and giving yourself the inclination.