The paper does not say there was a "conversation". It states '[t]hus, the temporal dimension of time matching can be an essential element to a conversation’s structure.' That is, that there was a noise made, and the animal echoed/made noise back a few times. My dog does that. My neighbor's green parrot does it. Alas, it is not a conversation.
Good luck to the Whale-SETI team though!
Still, when I make noises to my dog and he makes noises back there is definitely information being transmitted that's interpretable by both parties. So there should be some word that can be used to describe that exchange. Anyway, it's hard to tell from that paper (this is not my field, by any stretch of the imagination) if the Cetacean actually knew or understood that it was a human machine making those calls and not another Cetacean, which would probably be pretty confusing. In any case, this is still a step in the right direction so good luck indeed!
No, they didn't discuss the finer points of Hume's philosophy. It was just the "first" conversation, after all.
Are those ideas? No, but I’d argue they are equally and sometimes more important than ideas.
That type of meta-communication is most of the substance of many human conversations as well, even if the two people are talking about the finer details of weather or whatever.