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Yes non electrolytic caps work too.No difference for optical switches, its the wires to the switches which are the antennas picking up noise.
You need to increase homing pull off - when homing fails its usually because its trying to pull off the limit switches and doesnt pull off far enough for the switch to open again. Try increasing homing pull off to 3mm and then home again..
No, use caps larger than 5V, always over spec the caps and consider that the noise voltages are likely higher than the logic voltage. Also its 0.47uf not 47uf! 47Uf would take way to long to recharge after being discharged and so when the homing cycle moves off then back onto the switch the state would not have had time to go back high to 5v and the homing cycle will fail!
yes, they all share a ground at the arduino side and so can also share a gnd at the switch end as well.
Not in all cases - as I have recently spend a little while troublshooting!https://media.digikey.com/pdf/Data%20Sheets/Lite-On%20PDFs/LTL-4266N.pdf
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