1) What is the preferred method direction for airflow?
Depends on the case and HSF too much to say for certain.
Most cases have a general airflow from the front to the back, sometimes also from the side or towards the top or bottom, so that´s what you have to fit the cpu HSF into, preferably causing as little disturbances or unmoving hotspots as possible.
With a classic HS, it´s usually simple, the fan should just blow at the HS, and if you have a side duct providing it with cooler air from outside the case, so much the better.
With a HS where the fan is on the side or above/below, it should generally be mounted to push air upwards or backwards relative to the case.
2) Is the direction of airflow contingent upon the type of heatsink that is used?
Yes. Nowadays, most that have optional ways to mount the fan will include instructions on what mounting is preferable, some also show what is ok and what mounting direction should not be used.
3) Is their a significant difference in CPU temp if the fan is pushing or pulling?
With any sort of HSF where the air isn´t restricted in where it flows, having the fan pushing air at it is nearly always much better. If the HS itself uses ducting, a sucking fan can sometimes work as well, and very rarely, better than a pushing one.