Hi,
for this circuit, the gain of it can be expressed as: gain=gm*Rl, where gm and Rl are transconductance of the input pair and load resistor, respectively. So, if you change the tail current, gm value will change with it, so the gain will. and as to the bandwidth of this circuit, the mail pole is located at the output of the amplifier, so the bandwidth is determined by the Rl and parasitic capacitance of the input transistor, so it will not change with the tail current.
Hope it helps!