Pete, I've always maintained that Michael's animosity directed at Tom was due to Tom's failure to protect the family: i.e., Vito's near death and Sonny's murder, as well as the temporary decline in the Corleone power.
As far as post-Kay female companionship, I'm sure that he enjoyed some. However, I think Mike was pretty much a monogamous type and minimized his liaisons. As far as his Catholicism went, I don't think that entered his mind until repentance became one of his priorities