Hello, @Kris,
1.I have checked your site and there is no issue the ajax shopping cart sidebar is working fine, watch the complete video for better reference: https://www.veed.io/view/393aa2df-3952-45e2-91e6-95bd0920146e?sharingWidget=true
2. I have also checked your site on my android mobile and there is no issue, the mobile menu sidebar is working fine watch the video here for better reference: https://www.veed.io/view/92976da3-b557-4887-b21f-b68a129bad89?sharingWidget=true
It must be the cache issue only at your end nothing else, please try to clear your site and browser cache and check back or try to check on any other computer on a fresh new browser.
Regards 8Themes Team.