Do airlines allow you to bring food onto flights?

Most airlines do. The issue these days are liquids; many countries have restrictions about bringing any form of liquid (and creams or gels) on airplanes. Check with your airline before the flight. As a general rule, if you purchase a drink or liquid of any type after you pass through security you will be allowed to take it on board the plane. Remember, however, if you are on an international flight you will more than likely have to be screened again when you land, even if you are connecting, and they probably will not allow any liquids larger than 100ml or 3.4 fl oz through the checkpoint.

Yeah, these days you are not allowed to bring food and beverage past departures, however, if you bought your food in departures lounge, it would be allowed.