Hi,
Only I want to say, please keep it simple.
Why do you need 3 headers, actually? You can use a single one and then modify it with responsive mode if you do not want all the columns in mobile view or vice versa.
Explanation: when you remove the predefined header, then logo disappears, becaause the HEader section in your layout, you kept only menu, and menu right module positions. if you add logo column there also, then you will see logo as well!
You may recheck the documentation on 'Custom Header' so it will help you to get the idea about how to rearrange logo, menu, and other module positions in the columns there.
https://www.joomshaper.com/documentation/helix-framework/custom-header
This layout doc will help you to get the idea of reponsive section here:
https://www.joomshaper.com/documentation/helix-framework/layout-builder
If still anything is unclear, then let me know, I will try to explain. Moreover, you can share example of what you want in your desktop header and what in the mobile header, so that I can help you better.
Best Regards