Does it produce an electrical short for B=1 (5V)
I'm afraid this is an example of muddled thinking about short circuits.
For clarity's sake, assume the diodes are ideal, then, the input B can never be greater than zero volts; B will never = 1.
The input B is a short circuit for current into the anode and an open circuit otherwise.
With a real diode, B may rise to a few hundred millivolts.
Regardless, B cannot affect the rest of the circuit. Vout is independent of whatever is connected to B.
Does the following transistor circuit represent a logical NOR
I'll answer with a question: If, as is shown, the base of the right most transistor is connected through a resistor to ground (0V) along with the emitter, is there any way to turn on that transistor with A and/or B?