Is there an app to use a remote

That icon brings me to the calculator

The Calculator is a different icon.

You can edit which widgets are in Control Center, from Settings.

I can’t find the my home app

You don’t need the Home app on your iPhone (iOS 10 or later) for this use with the Apple TV box. Only if you have an AirPlay 2-compatible smart TV, and want to use it there.

What is your model iPhone? What is its iOS version? Models with older software may not have this widget (by default). You will need iOS 11 or later to get this widget. You will need iOS 12 or later to have this widget installed by default.

The Apple TV Remote in Control Center works only with Apple TV 4K, Apple TV HD, Apple TV (3rd generation), and AirPlay 2-compatible smart TVs. This means the widget can’t be used with the Apple TV (1st or 2nd generation). Identify your Apple TV model - Apple Support

Set up the Apple TV Remote on your iPhone, iPad, or iPod touch - Apple Support

Yes, depending on your model. It’s not in the app store right now to download but should be installed on your iOS device in the control Center

If the icon isn’t in your Control Center, you can add it in settings - Control Center