In terms of Aragorn's initial refusal to lay aside his sword when requested by Hama, I have always been on the latter's side for the reasons he gave. The point of the Oath of Eorl, as envisaged by Ruling Steward Cirion, was that Eorl and his people would be given Gondorian land in 'free gift', with the freedom to have their own laws and customs, and their own rulers, the alliance with Gondor being the only constraint on them. But that constraint would be the same on Gondor and its people.
In terms of what you think Saruman might have said to Théoden,
Boromir88:
I think it likely that Saruman would try to make it seem like Rohan was isolated from their Gondorian allies though. And in that way, with his offer he could press his own friendship. I agree there wouldn't be anti-Gondorian sentiment, but there would probably be a "You're isolated from your friends Théoden King, but I can help you."
I think he might have phrased it that it would be
quicker for him to aid Rohan, with aid from Gondor taking longer. He would certainly not have suggested that the Gondorians wouldn't keep their word, because they had a record of doing so.
I was amused, like yourself, by the fact that Gandalf was rescued due to Saruman hiding his intentions from Radagast.
I agree that Saruman was unable to completely fool Galadriel, who sensed something was 'not right' in his makeup; but he was still able to fool her into believing that he was an ally, as he had with others (except Gandalf), until September 3018.