LED has 3V Fwd voltage Drop

That assumption is actually far more complicated than it is stated above. Most of the times, people make the highly simplified assumption that a led will drop 3v once it starts to conduct (aka as long as If > 0). A real led starts to conduct at Vf > 0 (when If is very small).

1. In the following figure, what would be the forward voltage of the LED? (& why)

Assuming that the led conducts, the voltage drop over the resistor is 5v - 3v = 2v. Its current is 2v/250ohm = 8ma. Which means the led is conducting. so we are good.

2. In the each of the following 3 figures

Assuming that the leds conduct. The voltage drop over the 2 leds is 6v, which means they cannot be conducting.

Assuming that the leds are not conducting. The voltage drop over the 2 leds is zero, which means there is current going through the resistor. which means the leds must be conducting.

We fall into a fallacy, cause by the assumption that the led only conducts when Vf = 3v.

The other cases are similar and fairly simple.