I feel like I should know this stuff (what is a Linguistics major good for, anyway?), but I keep going back and forth on it, so I'm going to ask you all.

Historically, how common is it for a language to go extinct when the society that speaks it is conquered by a foreign empire? The empire would want to impose its own language, but it must be incredibly difficult to legislate what people speak in their own homes and agrarian villages. Would they need enforced schooling to teach children the official language? Language police? Is it a completely infeasible concept to begin with? Would a creole or other new language form (in the manner of a Romance language or Middle English) or does that only happen once the empire has collapsed and eroded the class differences between speakers of the two languages?

For a language to cease being used is very common under the circumstances you mentioned. There are a LOT of examples of this in history. However, that is not quite the same as a language extinction.

For a language to be completely forgotten by all (except scholars) is a pretty hard thing to do. As in, not spoken or understood by the general populous...

Wars and invading/occupying forces have had the biggest and most lasting effect on languages (outside of nomadic behavior). They most often manifest into composite languages.

Even during the Japanese occupation of Korea, when it was the death penalty to be seen speaking, reading, or writing Hangul (Korean), they still managed to keep their language alive... though once the Japanese were gone, there was a lot of Japanese words forever infused with Hangul

Extinction of language is more common when it is caused by social elite behavior. Such as a language only being spoken by nobility or by priests. It doesn't take much in situations like that lose a language in the mix.

In short, invasions will heavily affect a language if the occupation is a long one. But, absolute extinction is really rare.

If a language is spoken and written by a powerful nation, it is incredibly hard to erase a language completely. There are people in the world who can read ancient babylonian and whatnot. But minor languages can be easily erased if conquered, especially if 'conquered' means a large inflow of population, as has been the case with the Han chinese' recent move to the west, thus threatening tibetan culture.

Alexander imposed greek and greek culture on the lands he cultured, thus creating a unified nation.. Of course, the whole successor thing kind of ruined that.

Good examples of languages being destroyed are gaulic and iberian.. Today those people speak spanish and french, both are essentially dialects of latin.

Still, it is possible for a language to survive. Noone knows where Basque is from, for example, and it is probably a very very old language. It has nothing to do with any other language known to man, except maybe Iberian as a distant relative.