This appears to be a continuation of a previous thread on the same topic:
https://www.zen-cart.com/showthread....37#post1352037 where at least part of an answer was provided (though the details of the necessary settings were not).
So, regarding Q1, which could be impacted by the template in use (suggest temporarily switching to one of the default templates to ensure observing the intended operation.), but for categories to be shown on the main page, the following settings are necessary though may also help if you post the settings you currently have in the associated configuration listings:
In configuration->Products Listing be sure to set 'Show SubCategories on Main Page while navigating' to 1.
Also in the same configuration area set 'Include Product Listing Sub Categories Image' to true to see the images, and look at the other similar settings related to categories in that menu.
In configuration->images, there are settings for the size of the related category images that may need to be adjusted if the category(ies) are otherwise shown, but the image is say super small.
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