"There are too many people in this place."
Two reasons: 1) I think you can't say "这个地方人“. You would need the 的, so it would be "这个地方的人“. Also, to use 太like that, I think you need 了after the adjective (太…了 is the structure.) 2)"这个地方的人太多了“ is grammatically correct, and it conveys the same information as the English sentence, given ("There are too mamy people in this place.") but it's not the best "translation" because it has a bit of a different tone. I think this is active voice versus passive voice. "这个地方的人太多了“ is more direct and active: "The people of this place are too many" whereas "这个地方有太多人“ is more narrative and passive: "There are too many people in this place." or "This place has too mamy people." Make sense?
这个地方人太多 is fine (and quite natural too if you ask me). You don't need 的 before 人 (in fact that would sound very awkward, at least in my ears) because 这个地方人 is not a single phrase here. 这个地方 is the topic, 人 is the subject. So 这个地方人太多 is literally: "as for this place, the people are too many."
I‘m afraid not. First, 中间 means “between, in between of”, so it really doesn’t fit at all. You need multiple things to be 中间. If you’re looking for a translation of English “in”, 里(面) is a closer equivalent – assuming it really means “inside” in the context in question.
But in this particular sentence that’s not the case. Rather, “in a place” is an idiomatic use of the preposition in English. Think of how you can still say “in this place”, even if “this place” is something you can’t be inside of at all, an open field for instance. In fact, all the preposition conveys is a general sense of location, so if you really needed a preposition (which you don’t here), 在 would be the right choice: 在这个地方.
And I guess 在 could be used here as well, however if you ask me, 在这个地方人太多了 doesn’t sound very natural to me. Usually people would just make the place the topic and then comment on it. So if you translated it very literally it would be something like “as for this place, there are a lot of people.” If you added 在 it would become: “As for in this place, there are a lot of people.” – Not flat out ungrammatical maybe, but without the preposition it’s much, much nicer.