How does Unstable set's "The Grand Calcutron" work with cards that interact with a player's hand?
The program is your hand, and effects that affect or care about the contents of your hand affect or care about the program while The Grand Calcutron is on the battlefield.
Mark Rosewater answered this question specifically regarding discarding as follows:

What happens if an effect forces you to discard a card while The Grand Calcutron is in play? Do you discard from your program?
You discard a card from the program. With Grand Calcutron on the battlefield, your hands are the program so things that affect your hand affect the program.

Presumably, &quot;things that affect your hand&quot; includes the rule instructing you to discard to hand size in the cleanup step, so an effect that modifies your maximum hand size would affect the program the same way they would affect a regular hand.
Similarly, an effect that requires selecting a card from a hand would have you select from the program instead, and anything that wants to count the cards in the hand would count the cards in the program.