Answer
a) Positive
b) CurlF is zero.
Work Step by Step
(a) Let us consider that $F=Pi+Qj$, then we have
$divF=\dfrac{∂P}{∂x}+\dfrac{∂Q}{∂y}$
we can see that when $\dfrac{∂P}{∂x}$ is positive, since the $x$ components of the vectors increases in length, as we move along the positive $x-direction$ and $\dfrac{∂Q}{∂y}$, is positive, since the $y$ components of the vectors increases in length, as we move along the positive $y-direction$.
This yields that the divergence is positive.
(b) Let us consider that $F=Pi+Qj$, then we have
$divF=\dfrac{∂P}{∂x}+\dfrac{∂Q}{∂y}$
This implies that
$curlF=(\dfrac{∂Q}{∂x}-\dfrac{∂P}{∂y})k=(0-0)k=0$
Hence, $curlF$ is zero.
