(1) There is a Lakeland bus between Parsippany and NY. It takes about an hour.
There is a bus from Parsippany to Atlantic City, NJ. Then you can take train or bus to Philly.
(2) Time in Philly is tight. Maybe your friend can drive you to Philly the night before and you can buy the friend a cheesesteak.
(3) What are you doing in Phoenix? Perhaps cut out a day and add a day to one of the other cities.
(4) Overall it seems well planned out. Just expect the weather to be hot.