1. Possibly, the stronger magnets i tested triggered the sensor from further away. There is no benefit to that. Because of the higher strength magnetic field everything is increased; sense distance, hysteresis distance, error.
My thoughts for "perfect" magnets would be small weak magnets. They pick up less crud and will give better accuracy and repeatability.
Even the weak bar magnets I used trigger the hall switch from 5mm to 7mm away, if I had used weaker magnets still that triggered it from say 3mm away the accuracy would be doubled.
2. The resistor is for "pull-up" use, it makes the sensor output a +5v when no magnet is near, and output 0v when magnet it near. It turns the sensor into "logic-level" output that can be tied directly into any logic input and means you never have to fuss with resistors later.
3. No, the resistor does not change the gap setting.
4. Sorry I don't have a good video camera right now, I will take a video at some point in the future.
5. Thank you, that is a REALLY COOL idea!
If the LED is soldered onto the sensor and clear plastic is used for the mount then it will light up when the magnet is near!
Apart from the cool fun factor that would be really valuable for setup and fault finding and would really improve the design!