All of these things are edited or enabled in the "Mobile Version Settings" area.
YourDomain.com > Mobile Version Settings
Here we will go over:
- Adding the mobile Header and Footer
- Removing the "Site Menu"
- Enabling the Custom mobile version menu and where to go to edit that menu.
See screenshot:

To add a mobile Header or Footer, simply add the content here and save.
To hide the Site Menu from the mobile site, check the box that reads "Don't show Site Menu".(you may do this and manually create links to certain pages you want to show on the mobile version)
To make a custom site menu for the mobile version you need to first check the box labeled "Separate Site Menu for Mobile Version". Click save. Then go to your "Site menu" area.

Once you enable the mobile version menu, you will be able to see the option to create a mobile menu in the "Site Menu" area. You can add and remove items as you would create regular menu items.
If you have any questions about this please feel free to contact support.