A Rotating 30-Degree Angle in an Isosceles Right Triangle

In the isosceles right triangle $OPQ$, $\angle POQ = 90^\circ$ and $OP = 2\sqrt{2}$. A point $M$ lies on the segment $PQ$.

1. If $OM = \sqrt{5}$, find the length $PM$. 2. A point $N$ lies on the segment $MQ$ with $\angle MON = 30^\circ$. For what value of $\angle POM$ is the area of $\triangle OMN$ smallest, and what is that smallest area?