Hi,
The carsouel is not moving because you have too few products displayed. The module only loaded 4 products and you've configured the products per slide at 4, so there is only one slide with all the products the module is supposed to display on the slide.
So the problem won't be solved with the update. The problem is that the settings of the module are not what you want them to be set at.
You want to increase the number of rows for example.
Regarding the width of the elements, you set a too big one which leads to the products getting out of the zone attributed for the modules area where you have the carousel. Because of that, the navigation arrows disappear because you have CSS from your template which set the width of the images to be dynamic and since there is not enough space, their width go to 0.
That issue will probably be solved with the new carousel system, however it should be easy to fix by properly configuring the width of the elements in the settings of your carousel module.