Answer : Yes it can be, and it will act like a normal PN junction diode. The characteristic of ZENER diode is exactly same as PN junction diode in forward Bias.
Answer : PN junction of zener diode is heavily doped than ordinary diode. For the occurrence of Zener effect the zener diode is heavily doped. If the zener diode is not heavily doped then Zener effect ... breakdown voltage is sharp. If the diode is lightly doped the diode will have higher breakdown voltage.
Answer : Yes dynamic impedance of zener diode vary.
Answer : Yes, Zener diode is a voltage regulator. Zener diode maintain constant reverse Biased Voltage. If the current is varying then also zener diode maintain constant voltage.
Description : How can you identify a zener diode?
Answer : It conducts current in either direction.