If you accidentally removed the icon for your App Store app, you can find it by looking in your App Library. If you've got Screen Time set up on your device, the App Store may be hidden if you're not allowed to make purchases. If nothing else brings your App Store icon back, you may need to reset your phone's settings.

Instagram doesn't make an app for the iPad. They do, however, make one for the iPhone that scales up on the iPad. You are probably searching only for iPad apps. Search for Instagram in the iPhone apps and you'll find it.

Instagram is a free photo and video sharing app available on iPhone and Android. People can upload photos or videos to our service and share them with their followers or with a select group of friends.