I am able to add multiple products so I don't know what that can be. Regarding the non-functioning remove item button, it looks like you have renamed your shop pages from their defaults, particularly cart and checkout. On my system the remove item button is on the cart page but on your it is on a page called checkout-3 page. Maybe WooCommerce is getting confused about which page is which. Suggest you find the cart and checkout pages in the pages list, note down any bespoke content, and then delete these pages. Remake the pages with WooCommerce / System Status / Tools tab / Install pages button. Next, double check the page names in the pages list match the page name settings in the dropdowns at WooCommerce / Settings / Checkout tab / Checkout pages. If the shop is now working you can rename the pages if you want step by step ensuring its working after each step.