5.4.1 The position eigenfunction

1
What is the one-dimensional position eigenfunction called?
2
Sketch it.
3
What is the three-dimensional position eigenfunction?
4
What is the coefficient of the eigenfunction for a given wave function $\Psi$?
5
Normally, the square magnitude of the coefficient should give the probability of measuring the corresponding position. Why is this untrue for position eigenfunctions?
6
So what does the square magnitude of the coefficient give?