And why would they only have the most basic instincts if they are frshly killed and turned? Why wouldn't other brain parts function just as effectively?

The transition from dead to undead is not instant, There is a period of 4-10 minutes between death and reanimation. It is thought that this period of the brain being without oxygen is long enough to cause the brain damage and resultant loss of higher function that displays itself in even the freshest of re-animates.

As to the head shot- you have to remeber than the entry wound may look like a neat hole, but the average damage a bullet does when in the skull cavity is enourmous. To be safe,military operatives are advised that 'Dum-Dum's' are to be used for maximum tissue and exit trauma.
Don't let the door hit ya' where the good lord split ya'