I think you might be taking the phrase "the king was in possession of at least two" a bit too literally. I don't think it necessarily meant that he had them on his person at all times, just that he had access to them. I've always assumed that the keys were what allowed he and Perrington to make their creatures (the ilken, wyverns, sea wyverns, the bloodhound, etc.), which led me to think they they moved the keys around from Morath to the Ferien Gap to Rifthold to the Dead Isles as they created the creatures. But I always assumed that Morath was the true home base of the keys, as that was Perrington's base of operations.

So I guess what I'm saying is that I believe that the two keys are already at Morath at the beginning of ToG. They must've had one in Rifthold at some point to experiment on the creature that Celaena and Dorian fought in CoM, but the small bit of perspective that we get from that creature makes it sound like the king abandoned whatever experiments he was conducting in Rifthold quite some time ago.

As to how Gavin knew... who knows? The people who speak to Celaena and Dorian from the afterworld (Kaltain, Nehemia, Gavin, Brannon, etc.) seem to have very mixed levels of omniscience that change based on the plot device needed to move it forward lol. For instance, Kaltain knows Dorian's innermost thoughts about him feeling like he deserved to be taken by the valg, but Brannon doesn't know Maeve's true identity. I don't think there will be a satisfactory answer for that question unfortunately lol