Sorry to hear of your problem with MI. I don't think getting it from Fragrancenet has anything at all to do with your problem, however. I think the sprayer thing is just a coincidence. There will be nothing magical about getting the bottle from Neiman's, except to overpay for it at $315.00, plus tax. I think I would just ask them to send you another one after getting the one back that you send them.
From your description, it sounds like you believe the bottle is defective and that is covered, whether you have sprayed the fragrance, or not. Just tell them what you said here. Call them, state the problems, and they should send you a shipping label that you can print and send back to them at no charge! There shouldn't be a restocking fee, considering you believe the sprayer is defective and think the cap doesn't appear new.
Good luck with it! I have never had any problem at all with anything I have returned to them.