The first is incredibly non-transparent to the player. You should be able to see everything easily from looking at the game as it currently is. Having a current impact depend on the state of the world that existed in the past (that has no current visible indicator anywhere) is a terrible idea.

The second and third: how do they interact?
In the same way that real life economic decisions are handled. Larger cities are going to have more of a demand for a product. Distance from the source is going to have an impact on the cost of delivering a product to a market, and hence the profit margin.
Distance isn't great; do you count ocean tiles?
Why not, provided you have the appropriate tech. If you can't trade over ocean tiles until Astronomy, then that gets factored in.
What about ties?
Another part of the formula kicks in. If 2 cities are the same size but one is a single tile further, the precedance goes to the closer one. In an exact tie, flip a coin. I don't see why you find it so complicated.
Read the first page of the thread, lots of problems with any allocation mechanism.
It's just a question of finding the proper formula.
You are suggesting a strict chronological order; you're suggesting that only the early cities you build will be able to access the resource, and that cities you settle or acquire later will be get resource access.
No, only those cities that exist at the time of hooking up the resource will get supplied from that particular one. Anything after that will have to wait until a new supply source is found.
Do the resource access of a particular resource is set forever and ever when the resource is first connected?
If that prevents the exploit of destroying your own improvement then yes.
How is that logical or transparent? Player's shouldn't have to remember the entire micro-history of the game.
Again, how is it any different than remembering which city has a Library and which one doesn't?
I severely doubt that a larger army will ever be not useful.
It would depend on the situation at the time. If you have enough soldiers to fulfill your needs for the moment, and still have a surplus of a resource, then it could be beneficial to trade off your excess for the time being. If your needs change later, then you simply cancel the trade deal and use the resource yourself.
Either you'll want to hoard the resources and not trade them, or you won't want the extra resources and so the whole cap system becomes irrelevant.
Since we don't really know how the finite resource system is going to work yet, it's kind of pointless to debate the merits of hoarding vs. trading.
If you absolutely had to make luxury goods limited, the easiest way to allocate them would be to have them automatically allocated to your cities with the most unhappy citizens (ie net unhappy faces - happy faces).
Well that could easily be another factor in the formula for determning where the resources go of course. You're carrying on as if I'm establishing a firm set of rules here. I'm merely trying to offer suggestions as to how to make the other resources finite as well. I just think overall it would be better if all resources were treated in the same way.