What is the THS deflection speed?
For the A320:


Conf 0/1 the rate is 0.3°/s
Conf 1+F/2/3/Full the rate is 0.7°/s


I haven't found any difference for A/P vs Manual flight.

In A319, THS freezes in the following situations:


The pilot enters a manual trim order.
The radio altitude is below 50 ft (100 ft with autopilot engaged).
The load factor goes below 0.5 g.
The aircraft is under high-speed or high-Mach protection.


In A320, THS freezes in the following situations:


The pilot enters a manual trim order.
The radio altitude is below 50 ft (100 ft with autopilot engaged).
The load factor goes below 0.5 g.


There are further conditions under which THS range is limited, let me know if you would like me to expand.

Source: A320 FCOM DSC-27-20