Hello, @raj,
1. Unfortunately we do not have such a feature in our theme for now, so this requires extra Customization for now, You can submit a request here https://www.8theme.com/taskboard/ , so our dev team read it.
2. The only possible way is to add the Categories Widget in the sidebar with the dropdown option, and then create a Static Block and add that sidebar in it, after that use that Static Block on the Blog page, I have captured the detailed video for you, please watch it here: https://www.veed.io/view/7364c53b-b5e9-4286-8194-9fe2f63fd694?sharingWidget=true
Regards 8Themes Team.