Surface integral over a cylinder problem

The small problem is that $\vec n$ needs to be normalized. But your bigger problem is that you are calculating the integral on the wrong surface. When you integrate $r$ from $0$ to $a$, and $\theta$ from $0$ to $2\pi$ (not $4\pi$), you are calculating the integral on the bottom cap of the cylinder, not on the side. So solving the first issue, $$\vec n=\frac{1}{2\sqrt{x^2+y^2}}(2x,2y,0)$$ Then the integrand will be $1$. For the second issue, the first integral is along the circumference, $dl$ from $0$ to $2\pi a$, and $dz$ from $0$ to $h$