UPDATE The formula has changed as of the March 2011 patch, it is now
(city population * 1.1) + (capital population * .15) - 1 for each city connected to the capital, not including the capital.
- The Machu Pichu wonder increases the modifier by 20%, to
(city population * 1.3) + (capital population * .15) - 1.
- Arabia increases the constant by 1, to
(city population * 1.1) + (capital population * .15) (thanks WillfulWizard).
The economic overview also gives a far better explanation of how it is calculated - in other words, this question is now trivially solved by simply looking at that economic overview :)
Original answer below.
Okay, I did a bit more testing, and bwarner's answer is almost accurate:
Each city, excluding the capital, provides (city's population * 1.25) + 0.01 gold per turn. Owning the Machu Pichu wonder increases the modifier by 20%, to (population * 1.5) + 0.01, for all the cities.
The capital does not provide any gold.
The 1.25 and 0.01 can be seen in the Assets\Gameplay\XML\GlobalDefines.xml file:
<Row Name="TRADE_ROUTE_BASE_GOLD">
<Value>1</Value>
</Row>
<Row Name="TRADE_ROUTE_CAPITAL_POP_GOLD_MULTIPLIER">
<Value>0</Value>
</Row>
<Row Name="TRADE_ROUTE_CITY_POP_GOLD_MULTIPLIER">
<Value>125</Value>
</Row>
The economic overview also demonstrates these values.
I couldn't find any other factor which affects these values, and I checked different difficulty levels, different distances between cities, different city route type (road vs railroad, road/railroad vs harbor), different city health and whether it is occupied. Looks like it's solely the population.
The Paper Maker and the Wat are transformed into a Library and a University. The other unique buildings I tried were destroyed.
I'm pretty certain that some classes of buildings are always destroyed, but there is probably also a random factor.
The XML files have some information about it, the probability of capture for the unique buildings is the following
Longhouse 66%
Bazaar 75%
Satraps Court 75%
Paper Maker 66%
Wat 66%
For the other unique buildings there is no value given, I assume that they are always destroyed.
Best Answer
(tl;dr version in bold)
There are many national wonders that require a certain building in all of your non-puppet cities, the National College being one of them.
If you complete the wonder and only then settle a new city, there is no problem - the wonder is still there even if the new city is missing the required building.
If you are in the middle of the wonder construction, the construction will halt, and you will be forced to choose a different production project. However, the wonder construction will retain its progress, so once the new city gets the required building (and that can happen immediately, if you just buy it), you can continue working on it from the point you stopped. Well, technically there is a production "decay" - I believe that if you don't continue working on the wonder for 50 turns, then it starts slowly losing progress. I always manage to get those buildings long before the decay kicks in, though.
As an aside, as far as I know, the production decay is not exclusive to interrupted buildings. If you just switch a construction project by your own volition, it also applies - the progress will remain for 50 turns (10 for units), and then decay.
This is different with interrupted world wonders; you cannot continue working on them, so instead you are reimbursed with gold.