Are there opinions that a ger cannot get smicha bizman hazeh? Does Rav Moshe Feinstien imply that women can, in principle, be rabbis? Can a woman be a manager in a corporation (assuming that men report to her)? What about a ger?

Is there a din of chezkas kashrus nowadays, when most Jews are not religious? If you see a man wearing a kippah and you don’t know who he is, does he have a chezkas kashrus? Even in the times of the Tanaim the tzdukim were a miyut hamatzui, right? Thanks, Daniel

According to the opinion that the psul of a goy for schita is related to machsheves avoda zara, what about a ger toshav? Thanks, Daniel