Q:

Using a 5v voltage regulator - Capacitors necessary?  Better options? 

I am very new to electronics.  I am learning as I go, and I haven't quite found the answers I need; when it comes to programming, I'm not afraid of mistakes as they happen constantly.  With electronics, though, I don't want to have to buy parts again because I fried them! 
I am trying to build something that has three different components in it: a 12-volt 4.3-inch LCD screen, a 5-volt Raspberry Pi, and a 12-volt custom device.  I've had the idea that I can split the power I need three ways from a 12-volt power supply: one directly to the LCD screen, another directly to the custom device, and one to a 5-volt regulator, thereafter splicing into a USB cable to plug into the Pi.  As I've been researching, I've noticed that people say that capacitors in the circuit before and after the regulator are mandatory to keep the current from oscillating. 
Question 1: Is this three-way split with the regulator a sound idea, or am I missing something?  I understand there is the potential to need a heatsink on the regulator.  That's not an issue for me if necessary. 
Question 2: Does my circuit require the said capacitors?  If so, what kind/quality would be best?  I know little about capacitors thus far.  Also, I came across this component while reading another question/answer here; maybe this would be better than a regular regulator? 
Question 3: Someone who is not extremely proficient in electronics but definitely better than me said that it might just be easier to use one of those 12-volt car USB charger devices instead of a regulator, which makes sense-- USB is a 5-volt world by nature, and I don't have to worry about splicing a USB cable for the Pi; wiring up the car adapter would be easy.  And I have plenty of room to allow for a car adapter; the box I'm putting all of this in will be relatively empty for how large it is.  Is this a sound idea?  Perhaps better/easier/safer for the Pi than using either of the beforelinked regulators and capacitors spliced to a USB cable? 
As for amperage, I'm still researching just how much draw the custom device and the LCD screen will need to make sure there is enough current.  That's not going to be a big issue, unless there is something I am overlooking about a regulator requiring a substantial amount of amperage more than it gives out... but I don't think that will be an issue.  I'm planning to get a PSU with a good amount more amperage than my setup theoretically requires-- just in case. 

A:

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.