Does the name of the store have anything to do with Ernest cline's book armada

Sorry to say it does not.

No

Armada was named as it was because "Big Spaceship Gang Games" did not have the same ting to it. (It is an Invader Zim reference)

No, the store has existed before that book and Ready Player One.

It's not a book store. They do have games referenced by Cline's first work "Ready Player One."