16 (15 points) On a piece of paper with a Cartesian coordinate system, draw a circle with center at point $A(-1,0)$ and radius $2 \sqrt{2}$, and a fixed point $B(1,0)$. Fold the paper so that a point $P$ on the circumference of the circle exactly coincides with point $B$, and connect $A P$ to intersect the fold line at point $C$. Repeatedly folding in this manner yields the set of points $C$.
(1) Find the equation of the curve $E$ corresponding to the set of points $C$;
(2) If points $S, T, M, N$ are all on the curve $E$, and $\overrightarrow{S B}$ is collinear with $\overrightarrow{B T}$, $\overrightarrow{M B}$ is collinear with $\overrightarrow{B N}$, and $\overrightarrow{S B} \cdot \overrightarrow{M B}=0$, find the minimum and maximum values of the area of quadrilateral $S M T N$.
16 (1) Point $B$ is symmetric to point $P$ with respect to the line $l$ of the fold, so
$$
C A+C B=C A+C P=A P=2 \sqrt{2} .
$$

Therefore, the set of points $C$ corresponds to an ellipse with foci at $A$ and $B$, and a major axis of $2 \sqrt{2}$. Thus, the equation of the curve $E$ corresponding to the set of points $C$ is $\frac{x^{2}}{2}+y^{2}=1$.
(2) Let the angle between $S T$ and the $x$-axis be $\theta$, then the angle between $M N$ and the $x$-axis is $\frac{\pi}{2}-\theta$, so $|S T|=\frac{2 \sqrt{2}}{1+\sin ^{2} \theta},|M N|=\frac{2 \sqrt{2}}{1+\cos ^{2} \theta}$. Therefore,
$$
S_{\text {SMTN }}=\frac{1}{2}|S T| \cdot|M N|=\frac{4}{2+\frac{1}{4}(\sin 2 \theta)^{2}} \text {. }
$$

Since $0 \leqslant \theta \leqslant \frac{\pi}{2}, 0 \leqslant \sin 2 \theta \leqslant 1$, it follows that $\frac{16}{9} \leqslant S_{S M N T} \leqslant 2$, so $S_{\text {SUTN }}$ has a maximum value of 2 and a minimum value of $\frac{16}{9}$.