To respond to your first thing: Correct the O is optional, and don't worry about the more complex version of "O genki desu ka" at this point in time. I know what your talking about and the phrase does exist, but it is much too early to worry about it right now. Please focus more on the basics before we start to delve into some good old keigo (super formal Japanese).
Second: Genki, Genki Desu, Watashi mo, boku mo, ore mo, genki da yo, genki da, and more are all splendid replies. Although what I want to challenge you to do is go find the difference between all of these.
Third: Depends on the person and the situation, if it was unclear to everyone who they were talking about they would specify it with the persons name. However if it is clear whom we are talking about they would not use the name. Although, this suite is geared towards beginners of Japanese and as such the average Japanese beginner might not be able to pick that up as well from context so they provide it just to help everyone out.
"The reason I'm worrying about this, is because I'm studying Japanese because I hope to be able to study or work in Japan for some time. And the person whom I mentioned before told me that when you're way to formal in casual/social situations people kind of shy away and think "Why is he talking like that?""
This is true, but I want you to be careful with wording it that way... if you are speaking politely to someone you are good friends with, it kinda gives them a distance feeling. If you are speaking to them in regular Japanese then randomly talk to them in polite Japanese if it is done properly it can be seen as a joke but also can be seen as a sarcastic response like "Oh since when did you become such a big shot!" kind of deal. Although is rather complicated and I myself haven't quite gotten this completely understood yet so please don't overly trust what I have to say on this matter.
"And I don't know if the course covers a 'tone down' of formality in later lessons. So maybe this question shouldn't even be asked before I was through?"
The course teaches polite Japanese pretty thoroughly and generally speaking this is a good thing. Although one tough thing is that if you have practiced speaking formally since you have began speaking Japanese it may be difficult at some point to remember to speak informally to friends and peers. Although the thing is if you don't learn to speak polite Japanese before learning informal Japanese that everyone you meet might find you too informal upon first greeting.
Although, one thing I HIGHLY DISCOURAGE is purposely excusing yourself with the excuse of "I'm a foreigner so they'll forgive me"... they only give you a little leeway when they don't know you. After a bit they are expecting you to get better in Japanese while you are in Japan so DO NOT think you have the complete freedom to make that same mistake over and over. You need to make sure you LEARN from your mistakes and overall just work at becoming better at Japanese.
The idea that they don't mind because your a foreigner is a misconception. The thing is, Japanese people do not usually express their feelings of discomfort or other negative emotions to those around them because it is consider RUDE to do so in Japanese culture. I want to emphasize that, they do not EXPRESS their minor discomforts because IT IS RUDE TO DO SO IN JAPANESE CULTURE.
Foreigner or not, they will become discomforted by such mistakes. I KNOW FROM FIRST HAND EXPERIENCE. What happens is they do everything they can to prevent any clue of the minor discomfort, and when they have finished talking to you... they kinda walk in the other direction hoping to not have to talk to you less often because they don't like being put in a position of discomfort.
This is an extremely obvious example that I did, but there was a group of 3 chicks at my Japanese high school and one of which was really easy to startle. In the US, it was under my understanding scaring people was like a bit of a practical joke. However, in Japan scaring the crap out of someone is a bit along the lines of poking someone in the butt as a practical joke in the US... they don't mix. (In Japan that's seen as a childish prank so it was a good example). So I scared this chick time and time after again. They told me she was easily scared after the first time, but because I didn't quite get the indirect message that was "SHE DOESN'T LIKE BEING SCARED AND NEITHER DO WE, STOP IT!" I kept scaring her randomly. What happened as a result is the group eventually started avoiding me, and when that still didn't get my attention it ended up where they decided to never talk to me again. Which literally does mean NEVER talk to me again.
Learning to read into these small hints is a skill set that may take some time to adjust to depending on what culture you come from and what your social skills are in that culture (I began with very limited social skills so hence why these kinda mistakes happened a lot).
HOWEVER, don't worry about it too much. If you over-worry about it, I did that too, it can be just as bad if not worse as under-worrying about it. In other words BE CAREFUL but DON'T OVERDO IT.
Unhelpful as that may be, it is something you must learn on your own really.