Where are features displayed after they are created? I just created a feature on one site for copying to another and on the site I created the feature it doesn't appear in the list of features, and I am sure I didn't delete it.

When features are created on a site as opposed to being installed do they remain in the UI or do they have to be installed as well to appear in the site's Features UI?

Is there a module that provides a UI for managing the Features which are created on a site but not installed there?
I think its important to know that essentially, Features result in modules that capture site configuration.

Fundamental differences in D7 and D8 with what Features is designed to accomplish with configuration essentially in Core.

However, if you create a feature and "write" as opposed to "download" the UI should show your saved configuration. This section of d.o gives some detail.

You may prefer to try downloading features once they are what you want, and commit them to a git repo.  Much safer and stable working this way in my experience.