Screen mirroring

If your TV is AirPlay-enabled, then it will be selectable as an AirPlay Screen Mirroring destination.

List of AirPlay 2-enabled smart TVs - Apple

AirPlay destination devices may need to be added to the Home in the Home.app (on iPad or iPhone), and be assigned to a room.

Add a HomeKit accessory to the Home app - Apple Support

If your TV is not AirPlay-enabled, then you will need to connect a streaming device that can provide AirPlay receiving functionality. That can be an Apple TV set-top box, or select third party device.

AirPlay functionality is separate from the Apple TV app, although there is overlap for supported TVs. It depends on the exact model, though.

No but you can use iTunes to stream to the Apple TV 4K box etc