how to do with demo site with one serial number and top header removal issue

Dear Sirs,
I like your theme very very much. It looks great and professional. I have two questions:

1. I put it in my demo site with its serial number. When I finish it, I need to copy it to my official website with different domain name.How I can do with only one serial number? I still need to activate two copies of website because I need to confirm the website is going well until all of them are okay and I will close the demo site. Would you please help me reply a solution.

2. I want to unable the top header in the mobile screen. How can I do it?

Thank you very much in advance for your reply.

Best Regards,
Nicole