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
few points:
the datasheet says part is internally current limited and thermally current limited, but no information is given regarding the limits, generally they will give Thermal trip point and Internal current limit at particular condition.
the maximum current given by LDO will depend upon the series elements current handling capacity also. basically we need to do thermal analysis.
Worst case Power dissipated across = VinminIoutmax-(VoutmaxIoutmax)-PQ(Quiscent Power). So, here if Vinmin to Voutmax difference reaching to min dropout voltage, we can have maximum current which will not exceed the Tj of the device package.
from datasheet, in section Electrical characterstics, Ilimit(Vout shrted to GND) is 300mA.
from Ruff calc, by neglecting the quiscent current (~4mA from graph in datasheet ==> 4*9 = 36mW) considering DPAK with thejaJ-A as 92
Vinmin =9V, Voutmax = 5.5V(USB), TA =25 (assumed), Tj=150(from datasheet) maximum current can give = (150-25)/(92)*(9-5.5) = 0.388A. AS we don't much info regarding current limit, and thermal shutdown point, also block diagram doesn't given any circuitry regarding current Limit, thermal shutdown, You can confirm these things from vendor.
There are very good application notes from different vendors regarding thermal analysis. http://www.ti.com/lit/an/slva118/slva118.pdf
I have seen sometimes people will take more current from LDO than rated, unless it will not exceed the thermal trip point, but most of the times it mostly transient current.
Last,
there is no chance of getting 500 mA from this regulator for your input(9V), Output(5V) combination.