1. If you wish to delay things so that you can sell your existing stock, you should suggest that the issue of infringement be sent to an independent mediator or arbitrator who will issue a binding decision on the issue of infringement. It will take time to set up a mediator or arbitrator, to hold a hearing and for the mediator or arbitrator to issue a decision. In the meantime, you can sell your stock. You should lay down that each side bears their own costs of appearing before the mediator or arbitrator and the costs of the independent mediator or arbitrator be shared. This is the lowest cost option short of engaging in litigation.
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3. Yes, they can say "NO" to both an arbitration and to a mediation. Essentially, they can immediately sue you to prevent you selling any more hair brushes. However, if they believe you will play ball, they may be quite amenable to arbitration or mediation. The arbitrator or mediator sets the timetable. So, once you agree on a mediator, there has to be meetings to arrange the procedure and timetable. Finally, yes, they can sue you for the past sales you have made. Essentially, they can sue you for all losses suffered as a result of your infringement.
4. You reply be stating that you are not certain on the issue of infringement. So your suggest that the matter be referred to arbitration or mediation, to an independent person who can deal with the issue of infringement. Suggest the form the arbitration or mediation will take and who you might appoint as a mediator or arbitrator.