Hi,
If you have 404 errors on the categories links, it means that you change the menu items structure in some way and didn't update the canonical URL of the categories to reflect these changes.
Empty the canonical URL of these categories and the links should work again.
Regarding the products not being displayed when you reach a category, it's either that there is a problem with the settings of the "products options" tab of your menu item, or that there is a problem with your Joomla template.
Try to use the default template of Joomla and see if that helps. Otherwise, provide a screenshot of the settings of the products options tab of your menu item.