I've thought a couple of things while reading all of these...and I want to say that this is a great idea. But I think that it's being torn apart. Scroll down to "What I'd Like to See" to skip my feelings on various points. See "Short Version" for the...short version.
No points. I think that taking diplomacy and putting it as a set value that you can do every so often is fairly pointless, if you'll excuse the pun. It seems childish to be told, "Okay, Sovereign, you've already talked to 4 people this week. You can talk to more next week" when I am the lord and master of a whole civilization. Likewise, diplomacy points wouldn't be as 'solid' as, say, gold or food points - when you use gold or food, the result is definite. If I make a soldier costing my 5 gold and 10 food, then I get a soldier for 5 gold and 10 food. Having a large chunk of my structures producing diplomacy points seems a waste, as the results are far from certain.
Regarding the 'value' of trading object, my first thought was back to an Alpha Centauri game. I met another person early on in the seas, and he told me, "I have a copy of Sister Miriam's map, want it for 50 energy?". While that was fine and dandy, Miriam was on the other side of the map, and I wouldn't have to deal with her for several scores of turns at worst, several dozen at best. In that case, the map had real value, but just not to me. Likewise, it could have explored 100% of the world, but the value to me is limited because I don't need to know 100% of the world at that time. It could be worth 20 points in terms of value overall, but worth 0 points in terms of me.
Regarding Diplomats as On-The-Map Units
This was done by TW, and I didn't much care for it, for a couple of reasons. One, it would require me to hunt down a certain diplomat, drag him across the world, and hope that I shouldn't be sending armies instead. Plus, they seems to just have no value. By the time I ran across another faction, it was pretty much, "Stay out of my way, I'll stay out of yours. Declare war and I'll destroy you, if you want anything come find me." I felt it discouraged diplomacy, less because diplomacy was important, more because diplomacy was just a chore.
Regarding Diplomats as Champions or Important People
This one is kinda nice, I think, but there's also the point that early game you would have to risk losing an army (albeit temporarily) for a gamble. While the gamble itself seems viable and shouldn't detract from it, I doubt that it'd be useful to strive for a long-lasting relationship with your also-peaceful neighbor(s) when you have only one champion to send scurrying around the countryside. Furthermore, as a Sovereign, I feel that my children and my chosen generals shouldn't be messengers. I think it seems tacky to turn military leaders into bowing-and-scraping ambassadors.
Regarding Instant (Telepathic/Magical) Communication
If I were a Sovereign, I'd hate the thought of sitting down to dinner after a long day of Sovereigning and have thirty minds suddenly batter my own with questions and requests. Likewise, if I were a military Sovereign, I'd hate the thought of giving anyone access to even a small part of my mind. The same with magic, such as teleporting a scroll somewhere - if I can teleport a scroll with a request, isn't it just as easy to teleport a nuke and blow the heck out of my enemy? This seems like a risky method with lots of problems in a war-torn world, from a lore standpoint. I'd use it only if there isn't time for anything else to be implemented.
What I'd like to see
Something akin to GalCiv 2's espionage. That is, I manually build a diplomat, and he goes into my 'diplomat pool' for distribution. The way I'd like to do it, though, is by manually making a diplomat, who would come out at a certain level. Let's say this...
I build a diplomat, Bob. Because I have no research regarding levels, he comes out at level 0. I want to send Bob somewhere, so I click on him in the 'diplomat' or 'diplomacy' screen and click 'deploy'. From there, I can send Bob someplace after he travels there (negating instant communications). Once he arrives, I can communicate with Bob as much as I want, and Bob sees to it that whatever I want is relayed. That is, I tell Bob "Alright, I'll trade them Advanced Fishing for Horseback Riding." Bob tells them, they deliberate, and a few days/turns later Bob speaks up and says, "They say throw in 15 gold and you've got a deal." For completing this transation, Bob gains more XP, and thus becomes level 1. With a more difficult transaction (more back-and-forth, perhaps) Bob would have gaiend level 2.
However, what if I don't want Bob to be level 0, and I don't want to spend an eternity researching techs? Well, when I click on Bob, I can also click on another button called 'study'. In essence, Bob goes to study diplomacy in the city, and depending on the city's research output comes back swiftly (high research, or lots of academies and the like) or a while later (Fewer research/academic structures) at level 1. Doing it again nets him level 2, 3, 4...etc. Thus, it may help to train Bob up a bit before sending him out, but at the end of the day Bob will learn more through practice than through study.
So long as Bob stays in that faction's place, he and I can communicate with each other, and he can tell them my wishes. If Bob dies a horribly painful death, I can't communicate with that faction anymore until I make a new diplomat.
Another thing that I just now thought up...a sort of diplomatic influence. If Bob has spent the last 150 turns in my now-ally's city, he's likely to have more influence with them than, say, that brand new diplomat I just made yesterday.
1. Build a diplomat manually, deploy him with a click of the mouse on a place, and he travels there invisibly (that is, it takes him X turns to get somewhere, and he gets there when he does, no map interference)
2. I can also train my diplomats, helping them gain levels so they function better.
3. Diplomacy tree techs would allow for higher level initially for diplomats, as well as open up specific options.
4. Having the same diplomat in the same place for a long time will net improved benefits with that faction, as clearly you and the diplomat both care to have been there for so long.
That's my take...phew. Long one!