No menus being displayed in SideBar First
First of all, Menu works on the sidebar.

For your case, it's definitely the 'Permission' issue.

Permission for menu items: For example, you have only 'Add Content' item in the Navigation Menu. When you are logged in as an admin you have that menu on the sidebar as you have the permission to add a content. To display this item to authenticated/anonymous users you have to configure permission from 'Admin Menu' > 'People' > 'Permission'. Please check the permission of your menu items and configure as required.

Permission for Blocks: By default menu blocks have no permission restriction. Please check your menu block's permission section from 'Admin Menu' > 'Structure' > 'Blocks' > 'Edit' the specific block > 'Permission' tab at the bottom.

I hope it will help you.