"I already finished reading this book."
How do you know when to use 了 after 完. In ' I already finished eating lunch', it was not required.
Not really, especially since 读书 often has the meaning of studying, attending school. Also, 读 usually implies you read something aloud (though not always), while 看 is more about silent reading. So yeah, you 看书 more often than you 读书.