Hello,
Thank you very much for choosing our theme and contacting us.
Yes, for two domains you will need two licenses.
As for Header:
Please navigate to Woodmart > Head builder http://prntscr.com/iyd2pe
Choose the proper header type (your current) http://prntscr.com/iyd333
Modify elements as per your needs: http://prntscr.com/iyd3h3
Take into consideration that there is also the mobile view of your header http://prntscr.com/iyd3v3 check all the elements there.
If you have any questions feel free to contact us.
Best Regards