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I checked your store and find, yes there is issue as you mentioned in your post.
And reason its not working is your customization
1) If you check cart icon in desktop its not in its position and i think you make modification in html and that's why not its hidden in mobile too.
2) Impossible to add products to the cart, yes right away there is issue in it. Reason same, your modification. As i check in console there is no form tag outside product variant and button which is necessary.
If you fix these issue, both feature will start working as it was working before.