But is it possible that someone Mechalel Shabat will have a chazakah of being reliable on another field? For example, if he is known to be honest, does he get Kav Zechut on a money doubt?

No, he does not receive kaf zechut in monetary matters - or in any matter, for that reason. You need to understand this clearly: kaf zechut is only given to someone who is considered an adam, a decent human being, not someone who acts like a behemah, like an animal. A Mechalel Shabbat, according to the Gemara, the Shulchan Aruch, and everywhere in the Torah, is considered like an idol worshiper. He is not even considered part of Am Yisrael. To such an extent that you're allowed to charge him interest when lending money - something that's completely forbidden with another Jew - because he's treated halachically as a non-Jew. So even if this person has a reputation for being honest in business until now, if he's a known Mechalel Shabbat, you cannot give him kaf zechut. In fact, if you give kaf zechut to a wicked person, you're not doing a mitzvah. You have to assume the worst about him because he has a track record of being a rasha through his violation of Shabbat. The only people you give kaf zechut to are those who are righteous, who are Shomer Torah u'Mitzvot, who are known to be decent human beings. If someone is known to violate Shabbat befarhesia, publicly, he doesn't qualify for this benefit of the doubt, regardless of what his business reputation appears to be.