Hi,
Here is what I can see on the "product-listing" page:
i.imgur.com/LrK1EgI.png
However, looking at your screenshots I see why.
You need to turn off the "synchronize" and the "related products..." settings in the module. Otherwise, you're only showing the products related to products in your cart.
Regarding the carousel settings, you configured the module to load 4 products in the module, and to have 10 products per slide.
So that's why there is no carousel effect since there are less products than visible products, there is nothing to move.
I would recommend to set 4 in the "products per slide" setting. And then increase the number of rows to have something like 3 rows * 4 columns.
That way the module will load 12 products, display 4 of them at the same time and switch between the 12 products.