Hello,
1) There is a difference between Posts Categories and Product categories https://prnt.sc/5JkIDrrb6aP_ Which one do you want to add to the menu?
2) You can manage the order by option for the product categories widget in the Appearance > Widgets > Shop page sidebar > edit the Product categories widget https://prnt.sc/qN2ro2PV8TLh
3) What page does display the issue with the Elementor Pro plugin? Because I don’t see the problem while trying to edit the home page for example https://gyazo.com/f09027736c239e7c0121539365f68630
Regards