Hello,
To add the mobile sticky nav bar as shown in your very first attachment. You can enable it from Theme Settings >> MOBILE BOTTOM NAVBAR>> Enable Sticky navbar.
Screenshot: https://jmp.sh/LvtErcB
To add the mobile menu in your header go to Woodmart >> Header Builder >> Edit your current header and switch to mobile layout and then add the “Mobile menu” element and also checked the “Show categories menu” as in the screenshot: https://jmp.sh/YGb2PNM
To display the footer menu as like your attachment file. You need to edit your footer columns one by one from Appearance >> Widgets.and replace the list item content with the select and option tags.
Screenshot: https://jmp.sh/n6me6GH
Best Regards.