Are AirPods compatible with iPhone 7?

The AirPods should produce a popup on the iPhone screen when they are near it. And you can tap the "Connect" button. They do not show up directly in there Bluetooth Settings until after they are paired.

Try restarting your iPhone, and make sure the iPods case is charged. Link-> Restart your iPhone - Apple Support

If it still will not work, you may need to take them to Apple to get them looked at: AirPods and AirPods Case Service & Replacement - Official Apple Support

Yes.

Make sure your iPhone is updated to the lates iOS version, and follow the steps here to pair them: link-> Connect your AirPods and AirPods Pro to your iPhone - Apple Support