#1-The “Shopping Cart” icon on HOME PAGE product listings work and add the item in the header bar Cart total but doesn't show up in the cart box on the side or bottom of the theme. When I click the header bar cart total, then click “view cart”: the page says: There are no items in your cart.
#2-However, if I go INSIDE a listing and hit “Add to cart”, the item shows up on the bottom, side, and top bar cart area and items show up after hitting ” View Cart” in the top bar.
#3-It works also like above (#2) if I hit “add to cart” from store/products/
1. Please check if there's any plugin conflicts
2. check if your permalinks has been set to “post name” and “product base”
3. check if the WooCommerce pages are installed and set correctly.
If these doesn't help, replace the default theme and see if the issues remain or not and let me know the results.