if output is collector, Zout is very high only due to leakage // Rc of the current sink. (NPN) so Zout on CB and CE is the same but ends being just the load resistor only.
Base Input Zin=hFE*(Rbe + Re) where the latter is chosen to be larger than Rbe. So it can be high with a Darlington or low with Re= zero Ohm
Emitter impedance, Ze is the opposite of Zb input in that it is reduced by hFE unlike base input impedance explained above.
Ze = ( Rbe +Rb)./hFE
Rbe is the bulk resistance of the base emitter junction or incremental slope when saturated for Vbe/Ibe
When Impedance is low , like CB or gain is low (unity) like CC then bandwidth increases as voltage gain bandwidth product is constant at a specified current for each device type. (not all the same)