Although I haven't read the book from which the movie is "adapted" (in the loosest sense of the term, as I'm reliably informed), I can say that the movie makes clear that the action takes place in 1943. The opening scene is sometime in 1942 - then we move to Pearl Harbor "one year later".
As Mescator noted, the sub "looked at least like a Gato." My initial assessment was Gato or Balao. Then I caught the hull number in one shot: SS-395. A Balao. In fact, I was reasonably certain I'd had that boat in-game. I checked and, sure enough, it was the Redfish. I verified this on IMDB.
As for number of torpedoes, they actually got that right. In two separate attacks, the sub fired tubes 1-4 for a total of 8. While being depth charged, one of the torpedoes jarred loose and the motor started. That one would probably have been subsequently jettisoned, making it 8+1=9 from 24 leaving 15. Sure enough, in a bit of dialogue, the COB says something along the lines of, when has a sub in fighting shape ever returned to Pearl with 15 torpedoes.