editing category names

Hi,

You can change the names of the product categories or products yes. That won't break the links on the listings unless you've filled the "canonical URL" field of the products with the URL of the product and that the URL contains the name of the category/product and that you didn't specify the alias in the category/product or that you have a new alias.
For the product images, if you change their filename, you'll have to reselect them in the products using them as there is no system in the media manager to let HikaShop know that the file name has been changed.