Yes Steven...only one kind of tone: "ο tόνος." All the others are antiquated...just read the current books, you need to trust what you have in your hands, and go at it with concentration...I think ideally you can't expect your future teacher to explain little details often, not because it's annoying to them, they don't mind, but because it's not efficient for your learning, you will rather use them to practice what you've learned, which means as a rule there needs to be more time studying alone than with your teacher. Technically they should not be "teaching" you any material from scratch, you need to do that alone, and get that skills and improve it as you go along with what works for you. There just isn't enough time to go through a grammar lesson in detail in class, and plus you need the time alone to reflect upon the meaning, to patiently memorize, etc. Once you understand the topic at hand well, then you can freely practice this topic with a teacher, and they will challenge you by using this along with something else.

I recommend you study using the textbook "Communicate in Greek" (Επικοινωνήστε Ελληνικά). There are 3 levels, and it's an excellent way to work your way through the grammar. If you're beginning just get level 1, and then go on from there...it's great because it's a complete course, it's not superficial, it's contemporary, has grammar summaries at the end, answers to almost all exercises, and glossaries in 5 languages...I think it's especially important that it's designed to be like your speaking coach with its exercises. If you follow this, and complement it with whatever other material you find interesting, you'll all set.

Hey! If you are still looking for help in Greek, I'd be glad to help you, as well! 

5. Synthesis: You take your acquired knowledge and use it independently in a written paragraph, or short composition that has a more involved thematic connection. This phase is important in order to make a copy of your knowledge into long-term memory. You won't ever forget it because you'll remember it as being part of that story or context, and this association will remain at least for a couple of years in your mind if you review it from time to time.
As you can see, you only do phases 3 and 4 with your teacher in class. So the reality is that you do a bunch of times phases 1,2, and write notes. You get together with your teacher, and do a bunch of times 3,4 for the things that you studied. Then later alone, you do 5, the short composition, and have your teacher check it on his/her time. You send this to the teacher's email, they won't mind checking your little paragraph, it'll be child's play to them.
I hope this puts your studying sequence in perspective, and that it will propel your learning forward efficiently.

In language pedagogy, for any topic that you're learning, you ideally go through these learning phases:
1. Studying/understanding/memorization: you read the explanations, and model examples, by yourself until you have no doubts about how it works, and where it's applied.
2. Controlled practice by yourself: you do the written exercises within the given parameters. This is to check that you didn't misunderstand anything, and gives you the first opportunity. You typically check your answers at the back of the book. If after going back to the explanations, you still don't understand "why" the answer is what it is, make note of it. Take note of the syntax, or order of words if you think it's something that you couldn't have come up with yourself.
3. Verify doubts of your marked points with your teacher. Your teacher will tell you what you're missing, or if there is a mistake on the book (it happens more often than you think), or if there are multiple possible answers. Also ask your teacher about vocabulary you're unsure about. I use Google translate initially, to be fast at it...if things don't look right, I check at the Greek dictionary at www.greek-language.gr, the definition should have plenty of example phrases (overwhelmingly so!)
4. Unmonitored practice: Your teacher will give you additional speaking practice with the material but using a variety of topics, more vocabulary, and mixed with other grammar that you know already. The native speaker is able to do this off the top of his/her mind, and there is no reading at all. This provides a challenge that is necessary in order to take your acquired grammar knowledge into a more subconscious level. The teacher won't correct all your mistakes in this phase, but rather let you go on with your idea.