I don't know what you mean by the $20 Metrocard but if you are planning on getting a pay per ride for the subway and buses then you can use that Metrocard for the AirTrain as long as you have at least $5 credit. You will need a separate Metrocard for the LIRR.

As for street food some carts are conveniently located near public plazas which have tables and chairs, such as the 53rd Street Famous Halal Guys.