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Great instructable, but I think there are a few errors in your schematic. The RC filters you have on the comparator inputs look to be drawn incorrectly. The capacitor should be located directly on the comparator pin, so that the capacitor forms a voltage divider along with the resistor, to form a lowpass filter. As drawn, the capacitor is right across a low impedance source, so it will have little to no effect.
Your math is incorrect. The correct answer is R=V/I=(3.7V-2.0V)/0.05A=34 ohms for each LED, and if using a common resistor for all ten LEDs it would be 3.4 ohms.LEDs don't share current very well when put in parallel, unless all of their forward voltages are exactly the same. This might be the case if they came off the same die, but otherwise it is not. So, the LED with the lowest forward voltage, would take the most current.
Diodes dissipate the power as heat, just like resistors. Take the voltage across the diode, and multiply it by the current, and the result is the power dissipated as heat. The same measurement method can be applied to resistors, or anything else you put in series with the LEDs. Unless you are using a switch mode controller of some sort, this will always be the case.So, you are just moving the heat dissipation from the LEDs to something else, be that resistors, or diodes.