> Ohms law doesn't apply correctly to a "negative" voltage difference.
??? Sure it does.
However a silicon diode (or LED) does not have a simple number to plug into Ohm's Law.
I don't think you want the exact math. Anyway real LED's don't follow theory too exactly. But here are voltages and currents I would expect on a typical red LED:
2.0V 200mA (and death)
1.7V 20mA
1.5V 2mA
1.3V 0.2mA
The exact action at lower voltages is unclear, and varies in practice. It used to be common to find leaky LEDs: give them less than 1mA, they would not light at all, the 1mA of leakage just leaked around the junction. There are also some that act like several junctions, and will light weakly with less than 1.3V. But this is unpredictable.
Reverse voltage is not instant death to red or green LEDs. 5V is harmless. They "break down" around 7V reverse, but if the series resistor holds the current to not much more than 10mA they will not be harmed. They just don't light. A reversed LED without a resistor will burn up fast with more than about 7V, but remember that a forward LED without resistor will burn up fast with more than about 1.8 or 2.0 volts!
You might think you could just feed a constant 1.7V, but the current you get will vary a LOT with temperature, and once warm will probably go hot until it burns up.