"Before they open their eyes, how do they recognize their parents? How do they know their parents have arrived with food?"
Baby robins DON'T recognize their parents at first! When they hear a sound or feel a bounce from a parent landing on the edge of the nest, they have an instinct that tells them to pop up and open their mouth. Brand new nestling robins are so helpless that if it were a predator instead of their parent landing on the nest, they couldn't defend themselves anyway, and this instinct helps them to show their hunger so their parents will keep searching for food!

"How will noticing the position of the sun in the sky during the day when they're in the nest help these baby robins during migration?"
By noticing where the sun is in the sky from hour to hour and day to day, the baby robins are learning how the sky should look when they are home. Next spring they'll feel most at home when the sun is in the same place in the sky at the same times as it is here now. This will help them know when they are "home."

"How does this crowded nest change the family's nighttime sleeping arrangements?"
When the nest wasn't so crowded, the mother slept on top of the babies to keep them warm. Now the nest is too full for her to fit there comfortably. Fortunately, the babies are so crowded that they are keeping each other warm!

"Why do baby robins have fuzzy down on their heads when their other feathers are starting to grow normally?"
That little peachfuzz helps keep their little brains warm. Their bodies are all snuggled together, but their heads stick up, and are the part that could get the coldest.