"Этакомнатасзелёнымковромоченьтёмная."

I think that your point about there being multiple rooms with various carpet colors makes the most sense.

"Which room is dark?" "The room with a green carpet is dark"

My biggest problem isn't with "the vs a", but with "this".

First of all, it doesn't make sense at all in the above context. If you're specifying through verbal description which room out of several you're referring to, it can't be something within any reasonable proximity to you, so you can't use "this".

It also doesn't make sense within the context of the sentence. "This room" implies that you're near the room, close enough to see it. If you're close enough to see it, then saying "With a green carpet" is redundant. Everyone can see the green carpet. My original answer was thrown off; I said "This room is very dark with the green carpet" because it was the only way "this" makes sense. The redundancy is reduced if you're saying that the green carpet is what is making the room dark, because you're pointing out something about it beyond "It is in this room".

Admittedly, even if you replace "this" with "the", it sounds slightly off. I prefer "The room with the green carpet is dark" to "The room with a green carpet is dark". It doesn't have to do with knowing, but with specificity. You are referring to a single, specific room with a single, specific carpet. Saying "A green carpet" implies that it's just any carpet, it doesn't matter which one. But this particular carpet is necessary to identify the room; it can't be just any one, it needs to be that one. So you need the definite article simply to show specificity.

Now, all of this said, I can think of one context in which the sentence "This room with a green carpet is very dark", and that is informal oral storytelling. However, I personally don't think that informal oral storytelling should be a model for realistic/practical grammatical structure, and so I believe all my above points still stand. (In addition, "This room with the green carpet" still sounds better. I don't think there is any way to make "This room with a green carpet is very dark" the ideal choice for anything)

Also just quickly on the topic of "with the" and "with a". I am a native English speaker and they sound identical to me. I spent about five minutes pronouncing them out loud in various sentences and I am completely sure there is almost no difference. If anything, the "th" sound might be slightly softer in "with a", but at a normal conversational pace the two are absolutely indistinguishable.

The Russian sentence does not answer the question "which room is dark". If it did, it would be "Вот эта, с зеленым ковром". The thing is that, in the given sentence, эта means "that" ( the one we've been talking about or one of the rooms we saw in that house/flat). Also, ковер is more likely to mean a rug than a carpet so the correct translation should be "That room with the green rug is dark".

Don't quit!

I always feel weird responding when people clearly speak more languages than I do. (and I'm a little embarrassed that I'm basically monolingual).

Still, I was right there with you right up until you said: >But just thinking some more, phonetically speaking, "with a" and "with the" sound almost identical

And then I realized that I make the same mistake in other languages. I think it sounds the same - and it so doesn't.

I don't know what your native language is but, even when slurred by an English speaker, those two things are still clearly very different to us.

Quickly spoken the difference is:

"With a" - witha (tongue is soft throughout) "With the" - with'the The ' doesn't denote accent/stress but a break between two same sounds. The "th" from "with" would be slightly longer, then the "th" for "the" would kick in a bit firmer.

In any event, I think you know more about my own language than I do (and many others) so... I probably shouldn't have even responded.