why does the creature work so hard to learn their language? what does that reveal about the character?

He wants to understand the humanity which rejects him.

THis tells us that the creature is intelligent to teach himself how to read. This will factor into his judgments on humanity and his creator later on.

He desperately wants a human connection. He wants to communicate. Who doesn't? His own "father" has failed to teach him to speak, and he is not allowed normal human interaction in order to learn a language.