Who was the bastard and why?

I am a bit confused about the second episode's main plot.

Edmund, the Black Adder himself, was born nine months after the queen and some duke exchanged some steamy letters.

(Pregnancy really lasts for closer to ten months instead of nine, because the way it's calculated is a bit odd - when you calculate from the moment of conception, and utilize true months (instead of the Gregorian calendar), like the Asians often do, it comes to ten months and ten days, rather than the western-used nine months). But I am willing to look by this little detail.. obviously the writers didn't think this through (when do writers think at all anyway?))

The other son is born nine months before the letters were written.

But what does this prove? I mean, couldn't there have been an ongoing intimate-sexual relationship long before the letters were written?

ONLY if the letters were proven to have INITIATED the relationship, would it 'prove' that Harry wasn't the bastard.

However; this still brings about many questions. I am terrible with names, so let's call the king "Richard", and the man, who Harry's (or Edmund's) mother had sex with, 'Duke'.

So, Duke and the mother were happily doing sexual activities. Harry was born as the result. Then the mother had an 'affair' with this 'Duke' (and explains that 'what choice did she have, she was just a foreign girl' (odd, that a WIFE of someone powerful and influential would not have a CHOICE)).

Now, after this affair, things returned to normal, and either no one was the wiser, or Richard didn't care. How could this have been?

And couldn't Duke have blackmailed the rich and influential family, or the mother anyway, by threatening to reveal those letters?

There are so many questions that this whole thing brings, than are answered in the show, that it boggles the mind. Hard to enjoy a show that doesn't explain itself very well.

I mean, even in a comedy show, the plot should make at least sense, otherwise the floor disappears from under the comedy and enjoyment of it.

What I am wondering, is; if they were already happily married with Richard, why did she think she had no choice, and she was just a foreign girl? She wasn't just a foreign girl, she was a powerful man's wife!

If they weren't married yet, then how could Harry have been born before Edmund?

(Did women give birth out of wedlock a lot back then? And if it was true, then wouldn't Harry still have been technically a 'bastard'?)

I mean, none of this is very good proof one way or another in the show, and the queen's explanations just do not make sense.

Couldn't there also have been earlier letters, from before Harry was born?

It's just a very confusing plot point, the way it's presented in the show.