My feeling is (and has been since launch really) that the puppeting system/mechanic along with general colonisation is very simplistic and has a lot of room for expansion. The same could be said for the blanket "happiness" controlling a lot of growth and corruption settings where it might not be entirely appropriate. Health, war weariness and a much expanded political/diplomatic system, including much more depth to occupied/annexed/puppeted conquered lands would be more than enough for me.
Yes, but nearly all of these have always been true of Civ games in one form or another - they've never been simulations. Civ 4 maintenance was an extremely simplified way of dealing with a range of concepts from actual building maintenance to logistical costs of governance and the effects of corruption, for example. Occupying cities in past Civ games didn't even have a puppet option - it was simply a matter of annexing or razing, with a 'conquered' happiness penalty not dissimilar from the current one (only at city scale). Even the more detailed Total War games use essentially that simplified model, so I think it would be out of place to add much extra detail to that relatively minor aspect of Civ.
Health is a popular mechanic for some reason, and I wouldn't be surprised if something similar were to come back, if only because a lot of G&K seems aimed at appeasing nostalgia fans and if there's one piece of nostalgia that's still hard to shake, it's having some form of city-level management mechanic. I'm sure it could be managed in a way that allows both a global happiness mechanic and a level of city-scale management.
War weariness makes sense, but I don't see how to add it in a way that justifies an expansion or would make it any kind of big sell, and again there are plenty of higher-detail games than Civ that don't use any equivalent mechanic (such as Total War - which you might expect given the name, but the series is largely about empire management in the campaign map). Most obviously it would just be a happiness modifier, possibly also a production penalty that reflects the difficulty of sustaining a war over a long period. After all, it is only in the very recent modern era (and mostly subsequent to WWI, and particularly since the availability of mass media) that war has tended to cause unhappiness in a population in its own right, rather than indirectly through additional tax burdens, or through representing production losses which are arguably better-represented in other ways.
One omission that might seem strange, that has never been in a Civ game, is slavery. This is very much a key driver of civilisations' development historically, in many ways as much as the religion everyone wanted because it was so important to civilisation, and which is at least acknowledged in versions of Civ that don't use a separate mechanic for it. We get resources representing everything from spices (which had a major impact on the development of intercontinental trade routes as well as exploration) to tulips (which were a short-lived fad that made a bit of money for the Dutch), and yet one of the most important aspects of trade in history is essentially written out of the game. Certainly Civ IV had a mechanic called slavery, but it wasn't in any way related to slave trading or to the long-term impacts of slavery on both enslaved and slaver societies.
As for the question of whether there will be a second expansion, though, I suspect the answer is no. There aren't really any "big sells" they could use as a hook, with both religion and espionage in the game, to sell a full-size expansion. Health, war weariness and international trade are all good ideas, but not enough to sell more than a set or two of DLC. Most of the high-profile civs that were left out of the main game are in the expansion. The few remaining imports from older versions of Civ they could try, such as corruption or corporations, simply weren't popular.
