Your Color Settings are correct, good stuff.
You convert by going to Edit>Convert to Profile.
(Do NOT use the "Assign Profile" function, it's a menace).
Definitely DO NOT USE THESE SETTINGS. Stick to North America General Purpose 2 as it should be.
Yes, you can convert your images to Adobe RGB as part of the output process - either just before, or just after, sharpening for print.
Oh, interesting choice. Ok, I guess it can work ...
For the fountain, you'll need to work patiently with a low-opacity brush for the masking, to make it blend plausibly.
Sorry, that's as good as it's going to get.
But please be aware you're not out of danger yet. Not by a long way. When you resize for print or web, the problem might reappear. So make sure you've read this thoroughly.
Well, for out-of-focus ones like that, you might be able to clone it out entirely.
But where the grill is in focus, cloning would be prohibitively time-consuming, I'd say.
But I guess it depends on how much time you can afford on this job.
Opinions are completely irrelevant here. The only relevance is the print match.
Which calibrator do you have, and what screen? And which pro lab do you print with?