How to add sidebar to taxonomy page or node page? Thought a bit more how people use Drupal CMS to update categories. Categories will be taxonomies in a view so that they can refer nodes to the categories. 

Also at the most when click on category, it will be either a full taxonomy page or node page.

Sidebar will have taxonomy categories on left column and right column will explain more information. So if it is on same taxonomy, the menu item will be highlighted to let user know where they are on. 

The problem is how to add sidebar to either taxonomy page or node page and set menu item active / highlighted?
Normally I'd advocate writing it yourself, but in this case there are modules that do exactly what you want.

Create a block for the taxonomy you want to display and only display it on certain URL's (I'd use the path alias module to create a specific URL for relevant content e.g. '/CONTENT_TYPE/CONTENT_TITLEand test for/CONTENT_TYPE/*` on the block admin page)

https://www.drupal.org/project/taxonomy_block

You can use the Menu Trail By Path module to indicate what the active trail should be in the menu.