It's probably in Antony's interest -- just as it was in Octavian's -- to pretend that most of the senate was supporting him all along, especially with Agrippa and Octavian conveniently dead. I think you're right that Maecenas will meet an accident. The one other guy I think Antony would get rid of is Munatius Plancus, for ditching him in 32 and handing his will to Octavian. Isn't that the guy who supposedly also complained that Cleopatra was too powerful? I also wonder about the yunger Marcus Cicero: he wasn't really a threat, but I think he'd probably want to retire from public life.
The women are probably all right -- we don't see women being vulnerable to political murder until somewhat later, and they were not touched during either round of proscriptions in the Republic. Good idea to marry Julia off to one of Antony's sons, but I think it would be more likely to be the older than the younger, given Roman marriage patterns.
Yes, all of this. If you look at the senators who did choose to follow Antony up to Actium, they tend to be the older and more conservative/aristocratic ones. So he's clearly keeping up with Roman politics and looks respectable to the senate. Presumaby they felt that he was more likely to allow the return of republican politics. It is hard to see Antony returning permanently to Rome, though, given his behavior over the previous decade; maybe his goal was a strong alliance between Egypt and Rome, with his children by Cleopatra as proxies for that relationship. But it's really hard to say.
By this time, Antony's oldest son is not yet promised to anyone? He's what, 16, 17 already? The elder son could marry a bride from a patrician pro-Republic family, one of those that supported Antony even before Actium. This would be a good indicator to his allies that Antony wants to "restore the old traditions of the Republic" etc etc. Meanwhile, marrying his younger son to Julia is a move to reconcile with the pro-Octavian faction, I agree that likely Antony would have a general ammesty for the vast majority of senators and equites. Also good point about Plancus, that's another one on the kill list.
Does Antony have any daughters from his Roman marriage, I can't remember if he has a daughter with Octavia. Also, what happens to the marriage of Tiberius and Vipsania in this scenario, would it even go through, there's certainly no advantage for someone from the Claudian family to marry the daughter of an upstart who got himself killed at Actium.