What are some general guidelines regarding the halakhic permissibility for Jewish doctors to work on Shabbat? I know that saving lives generally overrides Shabbat, but I am curious about less black-and-white situations that may occur on Shabbat, such as having a shift where one must be in the hospital or be on call, receiving medical training, etc. Also, in a practical halakhic sense, are there any situations in which the appropriateness of violating Shabbat would depend on whether the patients are Jewish? I'm sure that these are not simple questions and that there are likely multiple opinions on various issues, but some insight into this topic would be welcome.
I'm sure there are several lectures on YUTorah.org about this; probably an article or two in Journal of Halacha & Contemporary Society as well. But in short:
"having a shift where one must be in the hospital or be on call" -- we generally try to avoid putting ourselves into a situation in which a matter of life-or-death might occur which would necessitating violating Shabbat; this "try to avoid" can be balanced out by other considerations, though. (That's one explanation given for why the Mishna prohibits getting on a ship too close to Shabbat -- a life-or-death situation may occur -- but if taking the trip is a mitzva, it's allowed.)
"receiving medical training" -- a tough issue, as usually the life-or-death situation must be fairly immediate, not "oh this may allow me to save some life out there someplace, ten years from now." Nonetheless, I'm told that Rabbi Dovid Cohen of Brooklyn has allowed people to take residencies that may require working on Shabbat. But check with your own rabbi.
"are there any situations in which the appropriateness of violating Shabbat would depend on whether the patients are Jewish?". That's easy. No. The Halacha is that we violate Shabbat to save any human life; that's the Halacha, that's the practice, that's what we do.