Dear Martin,
Sure, the compact layout should work on mobile as well. I logged in to check, but I think the problem was, that the final width was set to a % value on mobile, but the container width was actually not wide enough. I change it to a pixel value for your here: https://i.imgur.com/FVIGTrD.png
Now enabling the compact layout should work as well on mobile devices.
It is possible to change the magnifier and return button events here: https://documentation.ajaxsearchpro.com/behavior/return-key-and-magnifier-icon-click-actions