I’m having issues with the App Store I downloaded and app but it does not come to my Home Screen what is the problem?

Is it going to your App Library? Swipe left past your last home screen to get to the App Library.

See the information in Organize the Home Screen and App Library on your iPhone - Apple Support including the following:

To change where new apps get downloaded on your iPhone, or to show or hide the notifications that you see in the App Library:

1. Go to Settings > Home Screen.
2. Select an option such as Add to Home Screen or App Library Only.

Don't do it in Settings.

On your Home screen swipe from right to left to move to the next Home screen and keep doing that until you get to the App Library screen (it will have a search bar at the top of the screen with the words App Library).

On that screen, touch and hold the app and then slide it to the left to move it to a Home screen.

Does the following work? Go to the App Library (swipe left past your last home screen). From there you can touch and hold an app and slide it left back to the home screen.

Did you touch and hold it a second or two before sliding left?