How does heater's air-flow sensors work?
There are two thermistors. One is operated at low current (or at least low power dissipation) and is there to measure the temperature of the air stream.
The other is operated at a relatively high current (or at least high power dissipation) and has significant self heating. That thermistor will have a resistance that is related to both the temperature of the air stream and the air flow, as the forced convection draws more or less heat away from that thermistor.
The first thermistor is used to compensate the second one, so as to separate the two effects.

In answer to your second question, that kind of sensor is not very sensitive to air flow direction, though there might be some effect from the hot thermistor heating the air going to the ambient sensor and the shown PCB design will block air flow in certain directions.