2. I don't find that the statement "we do mitzvos because we believe that God commanded us to" is always either true or sufficient. Your assertion that a Jew ought to perform a mitzvah purely because God commanded him thus, and not on account of the consequences of its performance, may describe an ideal (I'm not sure), and it is certainly important to understand what one's religion considers ideal. However, in practice, I don't believe that most people follow most mitzvos for the reason you provide, and it is my impression that Judaism doesn't have a really big problem with that. It is my (potentially flawed) understanding that performing a mitzvah because one is afraid of being punished for sinning, or because one wishes reward for acting righteously, or because one wishes to become closer (read, connected) to God, or, perhaps, for other reasons, is a perfectly respectable, if not an ideal, religious act. I'd actually be curious to know whether any authorities say that the desire to become closer to God is, indeed, the ideal motivation; the notion sounds familiar. I'm quite sure I've been taught that every mitzvah we perform brings us closer to God.
I think your correspondent's principal error is not his expectation that mitzvah performance will connect him to God, or his implication that he is willing to perform mitzvos in order to achieve such connection (though I admit I'm suspicious). I think the problem with his question is that he implicitly assumes he ought to be able to understand how each mitzvah he performs connects him to God, when we don't fully grasp the process of connecting with God, or even, really, what it means in the first place. Jews believe that the Torah is a manual outlining how to become closer to God, which, again, dogmatically, is a good thing, whatever it is. If you assign the Torah validity, then you know (theoretically) what to do to make it happen. If not, you're on your own (and good luck to you). So while I agree with you that "it doesn't matter," what doesn't matter is how the connection happens, not that it does. You can give him the Torah's guarantee that the latter will occur.
It is also true, however, that if your correspondent finds one day that he's not motivated to perform mitzvos even despite the guarantee of increased connection to God as a result of performance, he's still got to do them. He'd therefore better have an alternate reason to observe mitzvos on hand. You're probably now thinking to yourself, "Right, that's why I told him we do mitzvos just because God commanded us to." See (3).
3. Another insufficiency I find with the statement "we do mitzvos because we believe that God commanded us to" is that it assumes a unobvious causal relationship between believing that some guy (let's call him "God") commanded us to do something and believing that we have a moral obligation to do it. I don't think your correspondent necessarily has that issue in mind, and I'm not especially suggesting raising it, but I think it's worth being aware that it is a philosophical hole in your writing (a pluggable one, mind you), and I'd say if you can avoid it with a bit of semantic maneuvering, do it.
4. I think the end of your "Part 1" has an incomplete argument. You say that explanations, etc., of mitzvos "must" be secondary, not primary (as motivation for performing the mitzvos). Now, to begin with, that can mean either that it is imperative that they be secondary, or that it is impossible that they are primary. It sounds as though you mean the former, which is quite all right. However, you need to tie up your theological loose ends. If one is motivated to perform a mitzvah because of some result, emotional or otherwise, of its performance, he may well, indeed, stop performing the mitzvah either if he ceases to detect the result, or if the result ceases to be sufficiently important to him. So what? Maybe at that point, that particular person isn't supposed to be doing that mitzvah any more. You've got to add in the fact that the Torah isn't supposed to apply only partially, or only to some Jews, or only some of the time. Since our particular person is supposed to be performing his problem mitzvah all the time, it is imperative that he have some stock reason for continuing to perform it, even if his "result-based" reasons fail. Back to (3).
(It may also be that since mitzvos are obligatory whenever applicable, it is logically impossible that such motivations as the explanations to which you allude ought to be the primary reason/s for any mitzvah's performance. I'm just noting that for elegance's sake; I don't think it's germane in the context of this discussion.)