Confusion about cutoff mode of NPN transistor
A)  I would agree with you, that the b-e junction is neither forward nor reverse biased, but that might be just a semantics thing.  From the diode's point of view there is no practical difference between applied voltages of +0.1 V and -0.1 V, but in my head there is.  Your results may vary.

B)  No.  Assuming an ideal transistor, one with zero leakage current, then if there is zero current through the resistor, there is zero voltage drop across it.  Note: there will be a voltage drop proportional to current going through Rl to whatever the circuit is driving downstream.