Looks like the SparkFun WiFi Shield is a clone of the official Arduino shield so it will probably work with the Arduino library and examples. The adafruit shield uses a different chip and would require a different library.
Does the button also needs 5 magnets (apart from the center magnet) or is 1 enough?
I expect the button will either need more magnets or a ferrous metal structure to concentrate the magnetic field into multiple poles. If you had 5 magnetic poles the magnetic field would fade out on all 5 sensors at the same time and then fade in again. You would not be able to tell which direction the disk was rotating. With a number of legs that is not a multiple of 5 you should be able to detect direction of rotation. I would try something with 6 legs.
It appears there is a central magnet to hold the knob in place an several hall-effect sensors under the knob to detect tipping and rotation. If you can buy a replacement knob and measure the pattern of magnetic fields that should get you closer to an understanding of how many hall-effect sensors are under that cooktop.
I think the laser diode package usually includes a photodiode that measures the light output so the control circuitry can adjust current to the desired output. Perhaps you should specify which laser diode you are using and what driver circuit you are using.
Question 2: Should I be slapping a diode from ground to the voltage reading analog inputs for protection?
That would only provide protection against reverse voltage by shorting out the battery. The diode would then die, followed by the Arduino. A diode in series would protect against a reversed battery but it would offset any voltage reading by the voltage drop of the diode. Use a voltage dividers to get the voltages being read down to a safe voltage (typically 5V or less).
The pin is fixed because it uses the Input Capture Pin of a hardware Timer/Counter. On the Arduino UNO there is only one ICP and that is Pin 8: ICP1. On the Arduino MEGA you can also use Pin 48 (ICP5) or Pin 49 (ICP4) because Timer4 and Timer5 have that feature.