Angela, your administration side will look just like the video. There may be some menu item differences, but the process to add or remove menu items is the same. WordPress only has one way to edit the menu and that is with the screen in the video.
To add a blog category to the menu, you need to first create the category and also have a blog post attached to that category, or else the category will not show up under the categories while adding to the menu.
Wordpress does not allow you to password protect a category, we do have a membership plugin that allows for what you are describing. Here is a link to the instructions for protecting a category: https://simple-membership-plugin.com/use-category-protection-membership-site/