How do I show this menu?

Hi,

You can create menu items via the Joomla menu manager. You can use the types HikaShop categories/products listing in order to have a listing of products or a listing of categories for the menu items.
The left areas with the menu items is a module called "menu" and is included by default in Joomla. You can create an instance of it via the "new" button of the Joomla modules manager and selecting the menu module. Then, select the menu where all your menu items for your shop categories are located and it will display it like that.

I don't know what you mean by "product category "chooser"" ?
If you're talking about the filters below the "BUY DIRECTLY FROM TEKNETICS" module, it is done with the filters system of the Business edition of HikaShop:
www.hikashop.com/support/documentation/1...-filter-listing.html