Tomche: The main Heter (which probably has issues for Sephardim because the Mechaber is against it, but I will admit to being unfamiliar with contemporary Sephardi Poskim and custom on the issue) is that the Rama holds that Pas Palter (baked by a baker for money) is Muttar. This is what many Ashkenazim and almost all Hechsherim without the “Pas Yisroel” label go by. The idea is that there is less of a feeling of closeness with a non-Jew who baked bread for profit rather than for you personally.
I would assume they have. There is a Gemara in Chullin (not positive on the Daf) that says that the bread of someone who eats Chometz on Pesach right after Pesach is not Chometz because they trade (bread according to Rashi, makes the most sense but has an issue with R’ Yehudah’s opinion elsewhere) with non-Jews right after Pesach. The Gemara says it’s Muttar for K’sheirim to eat, though I guess it wouldn’t be impossible to read the Gemara just from a D’Oraisa-Chomtetz standpoint. The word Muttar is a little weird though. I am not familiar if this Gemara is brought as a proof for the Pas Yisroel Sugyos or not.
One thing to add Moderator 42: The Halachah very clearly is that the Heter to eat Pas Paltir does not apply during the Aseres Y’mei Teshivah. During those days only things with a “Pas Yisroel” label should be eaten by everyone.