Basically if you excite a structure "back and forth" with a very high frequency comparing to its natural frequency the structure will not move.
The movable coil will not move in PMMC when the current is AC. In PMMC instrument if you pass an AC current, the current alternates/reverses very quick so the torque on the coils reveres too rapidly and the coil will not deflect. Only if AC frequency is too low you can see a deflection. That's why to measure AC with a PMMC you need to rectify the current.
On the other hand, if the permanent magnet's field is replaced by a magnetic field which is created by a coil through which alternating current passes, the field will reverse as the current reverses and the torque will be unidirectional so the coil will deflect. And this will be called an electrodynamometer instrument.
For the need of resistors(left circuit voltmeter, right circuit ammeter):
The coil will have some internal resistance Ri. And the voltage required for a full deflection will be Vo = RixIo. But for measurements with higher voltages a series multiplier resistor Rm is added. So we can write for the voltmeter:
V/Vo = (Rm+Ri) / Ri
Rm = Rix(V/Vo -1) ≈ Rix(V/Vo)
Same movement can be used to measure currents larger than Io, , by paralleling the instrument with a resistive shunt as Rs. With full deflection Vo across the meter will pass Io so we can write for the ammeter:
RixIo = Rsx(I-Io) then
Rs = RixIo/(I-Io) = Vo/(I-Io) ≈ Vo/I