Different Banner Image on Mobile (and hiding desktop banner)

Site URL: https://gar-grouper-xgll.squarespace.com/

Hello,

I would like to have a different banner picture on my coverpage for mobile 

I tried this code:
 

<style>
@media only screen and (max-width: 780px) {
    #page section:nth-of-type(1) { 
            display: none; 
    } 
  }
@media only screen and (min-width: 781px) {  
    #page section:nth-of-type(2) { 
        display: none !important;
    }
  }
</style>

Unfortunately, the first section (desktop banner) is still shown on mobile - why?

Also, I want both buttons to be black in the mobile version and to reduce the distance in between them (to make the upper button going further down so it won't touch the house) and to make the line under the logo visible like in the desktop version.

And I wonder why there seems to be a shadow box around the logo on mobile view 🤔

Hope you can help me!