I haven't been able to find any authoritative ruling on this anywhere, and the various People on the Internet who were talking about it had multiple different rulings, so I'd expect table variation.

At my table, I would rule that you can take a different skill (via the "if something gives you proficiency in a skill you already have you can pick another" rule that you quoted), but that the expertise would only apply to one of those four skills listed under Blessings of Knowledge (and you'd get it for the skill that you already had), so this isn't some backdoor way to get expertise in some random skill. That feels closest to the Rules as Intended IMO.

Yes.

Once you have the Prodigy feat, you have that additional skill proficiency. Thus, you can have expertise in that skill as well. The two occur simultaneously, but nothing prevents you choosing the new skill proficiency for your expertise as well.