Was The Movie "K-19" Accurate?

I just happened to see “K-19”, with Liam Neeson and Harrison Ford. A pretty good flick,but I wondered about the portrayal of the nuclear reactor accident. Are there any ex-Navy guys around who can answer these questions:?
-can a human actually enter the nuclear reactor compartment and live?
-the pump that blew up (ddoming the reactor)-is there no backup system for such a device?
-could a US Submarine survive such an accident?
-when you shut down a reactor, how long does it take to cool off?
-Finally, what are the state of Russian nuclear subs today? Are they still the deathtraps portrayed in “K-19”?

There is a historical kernel of truth in the story. From this article:

However, the film also recycles the horribly inaccurate myth that nuclear reactors can cause nuclear explosions, which ticked me off pretty good.

Here’s an extended account: K19: the story behind the movie.