Considering Joe had a stroke in 61 and was in a wheelchair then no he personally wouldn't do it, that doesn't mean he wouldn't have it done.
No, the fact that he wouldn't have it done is why he wouldn't have had it done.
As to who killed Marilyn, largely depends on which theory you believe leading to her death. The sad part is all of them are plausible and all those involved are dead today, so there is no real way to fully know 100% sure.
It wasn't the government nor the Kennedy's.
However my thesis is not incorrect in that if the American people find out about the overly sexed Washington there is no way they'd be reelected, as it is he barely won in 60. While Washington accepted it, it was not accepted behavior by the overall voting citizens (yes the late teens early 20s age group were sexually liberal to some extent, but not really even as nearly as much as often portrayed in media today, but they were far outweighed by their parents and grandparents in voting).
They won't find out, because even with those people in the media that did know, it was an open secret and there was a gentleman's understanding to leave it alone. Point two, I have to put my foot down here. Kennedy in 60 won by a close margin because he was a non-incumbent going up against an incumbent of a popular President; on the flip side, Nixon lost 60 because he had a charismatic risen star in the Democratic party as his competition. Regardless, 1960 has nothing to do with this, because you're playing it on the assumption that it means only half the country liked Kennedy, and the other half didn't, which is not the case. He had very high approval ratings. 1964 is not going to be as close as '60, and I am frankly very tired of the idea that it would be, which is something popping up far to often lately which is flatly and annoyingly wrong. '64 was going to be a massive blow out; to think Goldwater would even come close is dead wrong. And a sex scandal isn't going to come into play because there is never going to be one.
People who do this with JFK do so because he the sexiest toy in the box of history here. It's not based on the merit of it. It's based on the fact that JFK is the one you know for doing it. LBJ didn't have a sex scandal come up, and LBJ was banging women left and right just as JFK was. And yet, no mention of a sex scandal ever comes up for LBJ. That's because LBJ wasn't going to have one, and JFK wasn't going to have one. It's an old game he was taking part in.