Hello,

1.
Please navigate to Woodmart > Header 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.

2. You show the demo menu, and there is no HTML block that would reproduce this menu. It is our own customization

3. You need to create a menu in Appearance > Menu, then you need to add a Category element (please check 1) and select your created menu.

4. Please remove the background on the row in the Header.

Best Regards