I have created a page to simulate the problem with dummy data and uploaded it to my test server.
Sorry for lack of css, just wanted to keep it clean and simple.
I have also separated the search and results to make things clearer.
I have removed the default where string
Several things are apparent.
When adding items to the cart, selecting one or more item and a quantity will add those items (only) to the cart correctly.
If no items are selected and add to cart is clicked, all items on the current page are added to the cart.
On return to the results page, trying to add the same item to the cart again has no effect.
Link to the results page is here