Let's say I want to read the value of a resistor of X ohms (more accurately, voltage drop?). In my application I am using a 2 wire RTD, but it is essentially a variable resistor. According to my understanding the +5v pin is a +5v voltage source, it always supplies +5volts relative to GND. If this is the case wouldn't the voltage difference ACROSS the resistor of x ohms always be 5volts?
Yes! (Well theoretically yes. If the resistor is so small as to tax the current-supplying ability of the power supply, then the voltage will be less, and things may get warm, including but not limited to the resistor.)
Sure the current would change based on the resistance, but the voltage would not. From my understanding Analog Read gives the VOLTAGE at the pin. See the image on the left. Just for the heck of it, assume my resistor was 10ohms. What would analog read output?
Yes, and yes. 5 volts.
Now for my second n00b question. Is the image on the right a valid circuit? Basically can I use an external battery to send power through the resistor and read the value, or if I intend to do analog reads must power come from the +5v pin? Assuming the battery is 12V and the resistor is 10 ohms, what would analog 0 read?
The general answer in the spirit of your question is 12 volts, but practically, the Arduino cannot tolerate more than 5V, so some sort of voltage divider would be needed. The input pins have very high impedance, which means very, very little current will flow, causing very, very little voltage drop across the resistor. So in effect, the battery's voltage is seen at the input pin.
I know next to nothing about RTDs; the most basic approach would be a voltage divider where the RTD is in one leg, see attached schematic (not necessarily a practical circuit, just to illustrate the basic theory). I understand that RTDs can be very accurate devices, which means that some care will be needed in designing a proper circuit. This may include using very accurate resistors (not your common 5% type, but maybe 1% or even better). I also don't know how linear the response of an RTD is. If non-linearity needs to be taken into account, then some additional conversion work may be needed in software. Again, I'm ignorant, but there may be such a thing as an RTD interface device that will do a lot of this legwork for you. And they may use more esoteric approaches, like a constant-current source.
Hope this helps!