In case I do get a chance to babysit my nephew, how do you feed a young child when they're not wanting to eat at all, but haven't eaten in a long time, but the parents have said they're perfectly healthy?

I say trust that when they are hungry, they will eat. We try to force our children into set patterns that are acceptable by societal standards but we are each unique beings. They'll let you know what they need when they need it. Just don't believe them when they say they HAVE to have juice before they go to bed. :-)