Possible. But very rare. If you have problems with poor response to botox, most likely it is a bad injection, expired or diluted product, etc. Those who are 'allergic' make antibodies which neutralize the medicine before it an work. These antibodies can be detected with a lab test.
Very rare. Its theoretically possible, but extremely rare. I have treated tens of thousands of patients and have never seen a case. I have also never heard of a case being presented at a conference.
Yes. and also you ca develop antibodies to the medication causing it not to work in you as well. Speak with your doctor if you are worried about either to discuss what to do.
Possible. Yes this is possible but extremely rare.