Q. Can a religious Doctor who usually does not work on Shabbat but had to tend to a patient in a life threatening situation charge his normal fees to the patient? 
A. Shulchan Aruch (O.H. 306: 5) debates on hiring during Shabbos Chazanim and quotes opinions that when is done for the purpose od doing a mitzva it is permitted. Mishna Berura (24) mentions that one is allowed to pay a nurse that helped on a child delivery.
See also Shemiras Shabbos K’ (28: 75) quotes several sources for the physician being able to charge his fees in such a situation.
However, Horav Dovid Pam Shlit’a pointed out that Mishna Berura (ibid 23) also mentions that one who receives such pay will not see a sign of blessing and brocho from the monies collected.
Horav Aharon Miller Shlit’a disagrees in regard to a Yoledes. a saving lives Doctor or nurse.
Rabbi A. Bartfeld as revised by Horav Dovid Pam, Horav Aharon Miller and Horav Chanoch Ehrentreu Shlit’a