1. No. He just got done lying to God, so lying to Kay is no problem.
2. Some of the extended versions end with Kay in Church, lighting candles for Michael's soul, so obviously at least in those versions she believed the worst. Leaving that aside, though, I still think she knew that Michael had done these things. I think that from the very earliest moments of GF1 she enjoyed the excitement and exotic-ness of being so close to "the Family." I think that she was mostly interested in getting Michael to trust her with information.