Shop functionality comes from WooCommerce plugin. Shop page is a default one and can be only 1 – https://docs.woocommerce.com/document/woocommerce-pages/ but categories pages inherit the functionality of Shop. So you can create categories of products depends on your needs and add them to the Main Menu https://prnt.sc/ng4gdu
“Products per row on category page” you can set in Theme Option > Shop > Shop page Layout. Product Categories widget has an option to show “Only show children of the current category” that can be useful in your case.
Uncategorized is the default WC plugin category. Set another category as the default category http://prntscr.com/mo0uqt then delete the uncategorized one. Also, you can set “Hide empty categories” in settings of Product categories widget http://prntscr.com/mo0v82