I agree with your other points, but Stephen tells either his intelligence head or an Admiral why he wants Aubrey to command the ship that takes him intelligence gathering something like, “Give me two sticks that float, and Jack Aubrey to command, and I am confident of success.”
It is stated that Stephen has such a belief in Jack’s naval abilities as Jack has in his medical. (He can bring back the dead if the tide ain’t changed, and whip off a leg as kiss my hand.) Stephen at any rate believes himself to be an expert on things naval (is this not my left hand? Stephen, we are facing aft) and would demand on Aubrey from such reasoning.
Besides, while a dunce on land, Aubrey is a god at sea. 
I agree with both of these.
As to Sophie vs. Diana, bear in mind that Stephen loves Jack and wants him to be happy, but he also knows that Jack is a man who needs taken care of and would be better off with the domesticity of Sophie rather than the drama of Diana. Furthermore, Stephen thinks of himself as a loser doomed to a life of unhappiness, into which Diana fits perfectly.
As to the Oath, I don’t think we ever unequivocally see Stephen deliberately harm someone medically. Remember too that he refused to perform an abortion. My own view is that Stephen would kill in service of the war effort, but he would do so with weapons, not his medical practice.
He’s also been rather fond of Sophia from the start, and I think a lot of his encouragement was for her sake. She wanted the pairing, but with the obstacles in their way (Mrs. Williams! :mad:) she was feeling a bit lost about how to go about making it work. I think a lot of it was him trying to encourage her. I know there’s a quote somewhere in there where he tells her that Aubrey loves courage, and that if she’d only be bold about it things would work out. As it turned out, he was right and when she showed some spine and put her pride on the line everything did work out*. I don’t think he was doing that for selfish purposes, though I can see the argument for it.
…spoiler to anybody that hasn’t read the last couple books…
*Well, everything worked out except for Stephen marrying that horrible Diana. But at least a horse carriage fixed that problem eventually.
Oh fie, sir, fie!
He refused to perform the abortion on religious grounds, not purely medical ones. I’m a bit fuzzy on the details, but I believe Stephen was aware that he was actually endangering the woman’s safety by refusing.
If I remember correctly, her husband was impotent and was very likely to commit violence when he discovered that his wife was pregnant by someone else. And Stephen’s refusal caused her to go to someone less medically competent.
Agreed, but the Hippocratic oath also prohibits abortion, and I had the sense that it was at work in that instance as well.
Ok - I didn’t realize that the Hippocratic Oath specifically prohibits abortion.