I'm responding to the first query, "Is vocalizing the Greek words and sentences important?" being mindful that this is the Beginners Forum.
My answer is YES, for at least these reasons:
(1) Pronouncing Greek words and sentences out loud will help you learn faster and more thoroughly. You should listen to audio recordings, read along, read aloud as you work through exercise sentences, write out Greek in longhand... these activities will get all your senses involved and get the Greek "in your blood" so to speak.
(2) Pronouncing Greek words and sentences out loud will help you read the correct Greek letters, e.g. not mixing up nu and upsilon, not reading a p sound for rho, etc. Especially if you're studying on your own, these can be significant pitfalls at first, and checking your ability to accurately "sound out" Greek sentences against a good audio recording will nip such problems in the bud.
(3) It's just so very WONDERFUL to have Greek Bible sentences resounding in your head! I can still hear Ted Hildebrandt's distinctive voice (from the old "Greek tutor" software, which I used on diskettes back in the 1990s) enunciating εν αρχη ην ο λογος...
Other b-greekers also articulate reasons from modern language pedagogy, for using a more "living language" approach with spoken conversation back and forth in Greek; but as a solitary learner and online teacher, I have not explored these methods myself. These methods do seem worthwhile, for those who have the opportunity. But even if you're studying by yourself, you should definitely be "vocalizing the Greek words and sentences."
