Yes and no. If only a handful of members of that species exist, then then their disappearance would have a minimal impact on the entire ecosystem.
Well, by that point, most of the impact has already occurred. I read something once about how the removal of wolves from Yellowstone changed things. There were all sorts of repercussions all up and down the food chain. I don't remember now what all of them were, but I found it quite surprising.
It seems to me that most dying languages are dying precisely because their culture is already dying.
I'd guess that they both die at the same time, not that one death causes the other. And when you really get down to it, it's not like they simply died—it's that other languages and cultures have moved in and killed them, sometimes quite actively.
Using that definition of "die", would you say that Latin died?
No. Not in the same sense, anyway. Latin evolved and became other things. A language like Salish–Pend d’Oreille is going to go extinct and leave no descendants.