As far as I know, HOW COME requires its following sentence not to be inverted, while WHY necessitates the inversion.
Yes, that is correct. So it is completely normal that your sentence (a) confuses you, because there, you do use inversion after how come.
The standard statement is:
That is possible.
A question with why:
Why is that possible?
So indeed, you use inversion of is and that.
Question with how come:
How come that is possible?
As you said, no inversion.
If you do use inversion after how come, the sentence will be ungrammatical.
Where is my son?
This question expects that you (the person I'm asking) know the answer. It's a little more complicated than that, though:
- You might not know, but I am implying that you should know.
- You might not know, but I might be a panicked parent who (irrationally) demands answers from you anyway.
- I might be asking a whole group of people. Many of them won't know, but I'm assuming or hoping that someone will.
Do you know where my son is?
This leaves open the possibility that the answer is "no, I don't know". However, if you do know, it is still expected that you will tell me! If I ask this and you just answer "yes", I will think you are being deliberately troublesome.
In other words, this is an indirect way of asking the same thing. Indirect questions are generally more polite in English. That does not mean that "Where is my son?" is rude; it's just not quite as polite.
EDIT: As supercat's comment below so rightly points out, this question of politeness depends a lot on the context. If you should know where my son is (e.g. I've come to pick him up from your house), I would say to you, "Where is my son?" (Okay, I'd probably use his name, but that's beside the point.)
If, instead, I said, "Do you know where my son is?", you would have good reason to think that I was being sarcastic: I am implying that you are negligent, and so you might possibly answer "no" to my question!
Best Answer
Dan Bron's opening comment is correct, but I'd like to explain a bit more about why that's the case.
Basically, it comes down to tense and modality, or conditionality. Using "to be" (or in this case, "am") with an infinitive like "to know" is one of the future tenses English uses*, and it's a tense that expresses intention and plan. So you could rephrase "How am I to know?" as "What plan would you expect me to use to know this?"
Since that's a fairly common sort of thing to say, but "How am I to …" is a fairly formal pattern, it's not surprising that "How do I …?" has been adapted to that use as well informally. Formally, though, "do" is not conditional at all here. It's just asking for a explanation that matches current reality. So you could rephrase it as "Right here, right now, how is it that I know this?"
Obviously, both sentences (and both verbs) are very flexible, so there's a lot of variations possible, and a lot of different subtle implications depending on context. But that's the basic breakdown.
*To the extent that English has future tense, at least, which is the subject of some scholarly debate. Close enough, though.