From HAL's website:
"Explorations Café, powered by The New York Times: a comfortable, coffee house environment where you can browse through an extensive library, surf the Internet and check email or simply read the morning paper."
No, it's not free. There is an initial set-up charge and then you can either buy a package or pay by the minute.
Can't answer your question about which is cheaper - using e-mail or cell phone.
Enjoy the Maasdam.