1: Yes, you can do that. Essentially, that's how power supplies work. They can handle multiple parallel networks within their current capacity. As for the heatsink, that depends on the regulator, the current draw, the ambient temperature, how efficient it is, etc. It's not a simple yes or no.
2: The capacitors depend on the regulator as well. Some require them all the time, some only require them depending on the input or output conditions, some never require them. The NTE1960 you linked to does not have an extensive datasheet, but is pretty similar to the LM7805. The capacitors are pretty much required for stable use. But these are linear regulators. Not efficient and they convert wasted energy into heat. Going from 12v to 5v, at say 700mA which is the high end for the RPI, that means 12 - 5 = 7v * 700mA = 4.9 Watts of energy being converted into heat. A heatsink would be required.
A Switching regulator is more efficient, in terms of both energy and heat. The OKI-78SR component you chose is a Switching Regulator. It shows that it would not need a heatsink in that same situation (Not in the engine compartment though, that's a different story). It is also a complete module, including the capacitors and the resistors it needs. It would be better.
3: A Car USB regulator would work just fine for your case, as long as the draw on it is under it's maximum. Some are 500mA, some are 1A, or better or in between, but some can't actually supply the amount of current it says it should, so you would need to test. The Model B has a 700mA draw/limit, the Model A is 500mA. Most of these usb regulators are switching supplies, and for your purposes, a car usb adaptor would be exactly like the OKI-78SR. At 4 bucks for the OKI-78SR (plus shipping) compared to a few bucks for a car USB adaptor, it really just depends on which you can get easier. Even retail, you can get a decent car one at any convenience or auto store for 10 bucks.
You could even gut the car USB adaptor for the board inside. Those things are so small now they are smaller than a car cigarette lighter, with the case, and the size of an SD card without the case.
Best Answer
The 100 nF capacitor on the output is an important component for the stability of the regulator's control loop. It's not there to catch fast load changes; for that its value is too low.
A voltage regulator needs a short time to respond to load changes. This may seem like an imperfection but it's a requirement actually; a regulator with zero delay would not be stable.
Switching the reader on and off causes fast load changes. It won't be anything like 1 A/µs (which is damn fast), but fast enough to let the 5 V output sag for a moment. Russell calculated a value of 40000 µF to allow a 100 ms holdup, but you won't need that, the LM7805 will respond much faster than that (I would love to see more dynamic performance graphs in datasheets, especially step response!). For 200 mA steps a value of 100 µF should be fine. If you want to add a much larger value, like the 40000 µF it should be at the regulator's input, not the output.
edit
The guys at Diodes do include dynamic performance data in their AP1117 datasheet:
This shows an output voltage spike of a mere 15 mV for a 700 mA load change. The LM7805 is a much older design, and the figures won't be that good, but they give you an idea.
(end of edit)
I second Russell's suggestion for a series resistor to take most of the dissipation away from the regulator. At 200 mA a 56 Ω resistor will still give you 8 V input with a battery voltage of 20 V. The resistor will dissipate 2.25 W, so take a 5 W part for that. At 24 V in the regulator will have to handle 1.6 W, which it can do with a moderate heatsink. (Russell get a much lower dissipation, but he doesn't have any headroom in case the input voltage will sag.)