The chicks don't need food or water the first 2 to3 days but the hen needs access to it at all times, she may not get up to eat or drink but it still needs to be available in case she does. Simply place a chick feeder in one of the corners farthest away from the nest area and a chick waterer in the other far corner. Make sure the waterer is appropriately sized for chicks or has marbles or something similar to safeguard against drowning risks.
Make sure the dog crate has a fine mesh or something solid around the entire base to approx 6"-12" up the walls of it to prevent the chicks from squeezing out....they can get out of amazingly small openings but then forget how to get back in and the hen can't do anything to protect it or warm it if that happens.
Make sure the cardboard box has at least one side low enough for toddly chicks to get back into if they accidently stumble out of the nest the first day or two, their mobility levels increase rapidly after day one but they can only hop up very low amounts that first short bit. We usually just put a piece of scrap wood against the side of the nest to act as a step if they would need it, then remove it once they are mobile and bouncy.
Every flock is different in regards to safe integration, I have a couple of broodies who are never separated from the flock at all but I usually give our new broodies the first two or three days after they get up and about with the chicks and then let them integrate as they want...... BUT..... our flock is used to broodies with young chicks ....not all flocks are so friendly, so you need to determine what is best for your flock....
She's got a chick thanks to some of your advice (and others in here!)....such as not moving her and letting her set where she wants.
