The curve C has polar equation \(r^2 = e^{\sin \theta} \cos \theta\), for \(-\frac{1}{2}\pi \leq \theta \leq \frac{1}{2}\pi\).

1. Find the polar coordinates of the point on C that is furthest from the pole, giving your answers correct to 3 decimal places.
2. Find the polar coordinates of the point on C that is furthest from the half-line \(\theta = \frac{1}{2}\pi\), giving your answers correct to 3 decimal places.
3. Sketch C.
4. Find the area of the region bounded by C, giving your answer in exact form.