Hello,

1) I saw the screenshots you attached.

It is not possible to add the same menu in the sidebar but you can display categories in the Sidebar by adding the product categories widget in the Shop page widget area under Appearance >> Widgets.

Screenshot for Clarification: https://gyazo.com/5aea7456f21c62ff552b69288d443088

2) Please provide the URL of the website to check it myself and help you out accordingly.

Best Regards