Hi,

You can do all of that by add more this code to Customize > Custom CSS:

@media only screen and (max-width: 479px){
#header .inner-header{ background-image: url('YOUR_BACKGROUND_URL_PUT_HERE'); }
#logo a{ max-width: 200px; }
}

Note:

- Change YOUR_BACKGROUND_URL_PUT_HERE on above code to the background URL you want to change for mobile. Check this guide to know how to get URL of images you upload on WordPress.

- Change value 200 to value you want for logo with on mobile.

Best Regards,

PenciDesign