Discounted items in one category by listing

Hi,

Well, my answer would precisely be to make a new products listing menu item and activate the "discounted products only" setting of the menu item.
You'll also find in the menu item settings a setting to select the main category.
If you select the root category, it will display the discounted products among all the categories, but if you select a particular category there, it will only display the discounted products of that category.

Hi,

I don't understand what you mean.
If you want to have all your discounts in a category, then create such category and add it to the products with a discount and it will do it.