Adding social icons to header in mobile

Site URL: https://avocado-tangerine-n2wl.squarespace.com/

Hi there. I'm having trouble adjusting the mobile header on my site. I'm using Archer in 7.1. In my header on the desktop view and I can see my social links in the top right corner but on the mobile view the social link disappear. I know they are moved to the drop down menu but wanted to know if there was away to keep them in that top right corner in the mobile view. Is there also a way to make the X in the dropdown visible and instead of the white border, is it possible to keep the green image I am using as the site background?

If you use Business Plan, let me know. We can use some jQuery code to insert social icons.