An Ellipse Three-to-One Ratio

The ellipse $E:\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$ ($a>b>0$) has left and right foci $F_1$, $F_2$, eccentricity $\dfrac{\sqrt 2}2$, and minor axis of length $2$. Let $A,B,C,D$ be four distinct points on $E$.

1. Find the equation of $E$. 2. If $A$ is above the $x$-axis and $3\overrightarrow{F_2A}+\overrightarrow{F_2B}=\vec 0$, find the slope of the line $AB$. 3. If $C$ and $D$ are both above the $x$-axis and $CF_2\parallel DF_1$, find the maximum area of the quadrilateral $CF_2F_1D$.