This kit, which I have installed, does not support the intelligent heat management function of the N52 Engine where it modulates the coolant temperature dependent on the engine load condition. Is it supposed to support that?

Yes, these parts absolutely support it. The water pump is controlled by pulse width modulation from the DME on the bit serial data line (purple wire to pump) via a pulse width modulation signal. The control unit inside the water pump interprets the PWM signal on this can network which then controls the output of the water pump. The thermostat is controlled as an on off switch with direct power from the forward junction box with a switched ground controlled by the DME. The only way the water pump would not function on varied output is if there is an issue with the internal control unit (not likely on a new pump) or an issues on the bit serial data network. The operating modes on an N52 engine are 112C economoy, 105C normal, 95C high performance, an 80C high performance + mapped thermostat mode. These temperature ranges will also be affected by A/C or the heater being on.

Does this fit for 2011 X3 28iX USA Left drive?

No, this does not fit a 2011 X3. F25 X3 with the N52 engine uses an entirely different water pump and thermostat than what is used in the E83 X3. The water pump and thermostat kit can be found by searching p/n 11518635092KT.

Is this waterpump new or remanufactured? Do you sell remanufactured waterpumps?

The water pump is new.

How often should or what is a good rule of thumb for a Water Pump replacement on the E90's?

A good rule of thumb for this system is 60k miles.

What's the difference between the Pierberg water pump vs. the BMW unit you sell?

There is no difference. Pierburg (Continental) is the OE supplier to BMW for this pump. They are the same.