The magic shown in Constantine mostly, although not entirely, derives from real-world beliefs about magic and religion, although some spells, such as the sleep spell, are not clearly tied to any tradition. Although most of it derives from European traditions, some comes from Africa or the Middle East, or occasionally Asia or South America.
Among the ...
Well, just going off the list you gave, which doesn't include anything about Achilles (Greek legend), Solomon (Hebrew legend), or Pazuzu (Babylonian myth), you've got
Babylonia: capnomancy, exorcism
Christendom: Faust, grail, hand of glory
Egypt: Eye of Horus
Israel: water of the Jordan
It's not been revealed yet. You'll have to wait until episode 10 (assuming the show lasts that long)
The show's producer has explictly confirmed that Chas is not an immortal and that the reason for his resilience will be revealed farther into the series:
In a recent interview, the show's backers have confirmed that his apparent immortality is something ...