Hello,
First we can invite you to read
this documentation
and most precisely the Item Menu part, here
.
Maybe it will already help to sort out some points.
Now to answer you, more directly :
"If I select a category I go to a list of products (can I display the category and image)"
=> it's possible if you use an Item Menu, but you have to use the "Categories listing" for the Menu Item Type.
Then, in Categories Options tab, Item Layout part, define layout type on Image and title.
"if I select a product (can I display the category and image)"
=> Can you detail more your request through concrete case, description, or better an example please ?
Sorry for this last returns but we aren't sure to understand your need.
Regards
Philippe
Team HikaShop