Add a new category for posts

I`m new with coding in Wordpress.
I try to make a plugin with a widget.

When I install the plugin I want it to make a new category for posts.
I want the new category named GiveAway.

Name: GiveAway
Slug: GiveAway
Parent: None

When the plugin is finished, I should work like this:
When you install the plugin a category called GiveAway for posts will be created.
If I make a new post and select the category GiveAway, this post title and feature image will show in a widget at the font side.
Then you can click at the image or title to enter the post.

This category should only be visible for administrators at the backend, not other users. Only the administrator should be able to use / select it.

I think this category should be hidden for the visitors at the font side in URL and category list.