As I have always read it, when you extend your parma, you give protection, but do not forfeit absolute control over it. So my answers would be:
Yes, she can. However, she will have fto lower the parma that covers everybody covered by it (the whole force field) not only the bit covering the apprentice.
No, the apprentice is cozy and comfy under the protection fo the mystic blanket, but does not control it.
The form bonuses are personal, so the apprentice needs to lower those himself.
But, without knowing Parma himself, can he lower his personal Form bonuses? As near as I can tell, suppressing magic resistance, even your innate form bonuses, seems to be unique to the Parma. If a magus has no Parma, he still has his Form bonuses, and I don't remember seeing any other instances of anyone (or anything) suppressing their MR.