It is legal in most countries to listen to police feeds. However, it is illegal in some places to use this app to aid in the commission of a crime or to pose as a police officer when you are not. It may also be illegal to use it while driving. Please consult your local laws before using this app outside of your home.
It's very real. Each feed comes from a person in that region with an expensive police scanner sharing the signal with you via the internet.
The delay between the real radio feed and this app is only a few seconds depending on buffering and internet speeds.