Does the little boy im nanny for miss his mom and sees me as a kind of surrogate?

Yes. The relationship between nannies and their children can span the entire spectrum from indifference to pure love. It's a different type of relationship than the one that he has with his mom. In your role, it's always good to re-emphasize how much his mom is thinking about him, missing him, loving him, glad that he's having fun, and how she can't wait to see him soon. =).