You'll get arrested coming through customs on your way back.
Yes you can. A warrant means you need to surrender your self to police,therefore, it your at the airport and there is a warrant out for your arrest,then you can be arrested,thats f they find you, and the airport police may have details, so when you check into the airport, you might find that they will hold you and prevent you from travelling.
No, probably not
If you have an arrest warrant, you can't leave the country. If you choose to do that you are a person wanted.