Yes she is the Phoenix. No she was not born as the Phoenix, but her connection with the force has grown to such a degree that the Phoenix power is as natural to her as her telepathy. At this point and time, her "mutations" are: A. Telepathy B. Telekinesis and C.(her secondary mutation) To be the perfect host body for the Phoenix Force. Therefore, I'd say that at this point, Jean Grey without the Phoenix is like the FF without their powers. After all, the FF weren't born with their powers, were they.
Also, Jean's TK is so advanced and powerful, that there is no doubt that she could make an airtight bubble, although other telekinetics may not be able to do so, Jean is all-powerful in the world of telekinesis, she would be able to do it. (As for the refereces of imperfect shield-makers, you mentioned Unus, but his bubbles were airtight, Spiderman technically killed him once by not letting up on his attacks and Unus suffocated...)