QUESTION 1 -- Can someone please confirm that, referencing the attached (forgive my fabulous artistry) circuit diagram, I should be able to do a digitalRead(input_pin) and get HIGH when the switch is closed and LOW when it's open?
I direct you in particular to the fact that the power supply for the switched circuit is separate and independent from the arduino. it's just its own little 9v battery.
If we pretend you have a "safe" voltage (safe for the Arduino), say 3 AA batteries in series to give you 4.5V...
It can't be completely independent... You need a common ground*, then you can wire a battery like the [u]Digital Read Serial Example[/u]. But, you'd connect the switch to the battery instead of to the Arduino's 5V.
QUESTION 2 -- Do I need the resistor in the circuit? If so, QUESTION 2A - why? Is it only to prevent a raw 9v from feeding to the Arduino input? or do I somehow need the load to make the measurement work? And then again, why?
The resistor is needed when the switch is open to "pull up" or "pull down" the input.
That's because when there is no connection to an Aduino input it "floats"... It's undefined and it may read high or low. Its also very-high impedance which means very-little current is required to make the input high or low, it can pick-up electrical noise and switch between high and low.
When the switch is on, the pull-up or pull-down resistor is "overpowered" by the switch, which essentially has zero resistance. When the switch is on (closed) current flows through the resistor (higher resistance = less current). ...If you had a solid-connection instead of a resistor, you'd have a short when the switch is turned-on... Too much current would flow, voltage would drop to zero, and the power supply and/or switch might get "blown".
QUESTION 3 -- does it matter where I put the wire going to the input pin. Right now it's attached to point A, which is after the switch, before the resistor. Could I hook it up to point B or C ? I suppose I could breadboard that... but please answer me anyway.
Again, you need a ground reference, so you need 2 connections. The voltage on the Arduino's digital input should be (about) +5V or (about zero volts) relative to the Arduino ground.
You can connect through the resistor as long as the resistor is below the megohm range, because the Arduino's inputs are very-high impedance/or resistance (and because of Ohm's Law and Kirchhoff's Laws).
If you connect it backwards you'll have negative voltage (relative to ground) and that can damage the Arduino.
- Voltage need a reference and that's usually "ground". It's not necessarily earth-ground and the reference doesn't have to be ground at all, but it needs a reference. For example, if you measure height you need to know the height relative to something... Maybe the height above ground, or the height above the floor in the room, or the height above sea level, etc.
PLEASE DO NOT TRY THIS, but you can touch the power line voltage if you don't touch ground and as long as that there's not a current-path through your feet to ground you won't get a shock. With no ground reference there is no voltage difference so you no current flows and without a reference you can't even measure the voltage.