The consumption of the individual resources does not add up to the totals. Why?

That is because the individual consupmtion is not really a consumption but instead a needed minimal supply of that specific resource. The manual says this: “The total consumption of a type of resources is larger than the amount of the single needs. The additional request can be satisfied by any of the resources in that category. In this case this means, that each province requires 1.200 tons of food per province per day and 500 of these 1.200 tons have to be grain. It does not matter if the additional 700 are filled up with grain or with fish.” (See Manual –> Economics & Resources)

Please note: This has changed, the FAQ entry will soon be updated.

How does the stock market work?

On the stock market, you can exchange resources with other players (real ones and computers), without knowing who is buying from you or selling to you.

For an order to be executed, there has to be a fitting order to meet your demands. If you try to buy wood, for example, there has to be another player offering wood for less or equal money per unit.
You can see the pending orders for all goods on the right side of the screen. This enables you to create a fitting order to immediately settle the deal. As other players will see your open orders there, too, they may react to it.
Non-player characters will trade their demands and surpluses once a day for the current price.

Why can't I trade provinces or troops?

Both trading parties have to give each other "Right of Way" to exchange provinces or troops. If this would not be needed, the traded armies would start fighting each other right away as they would suddenly be on enemy soil.
To give someone else Right of Way, got to the "Treaties section" of the "Department of Foreign Affairs", check the box that says give right of way and press the apply button. (Remember that the other party has to give right of way as well to actually execute the trade.)
Note that if you want to make an offer to some other player where he/she should give troops in return, you've got to be able to see the troops you'd like to select. If you want to trade your own, you can of course select any units you like.