$7(1,2]$ Prompt: (1) When $F$ is on the line segment $C B$ ( $F$ does not coincide with $C$), from $|P D|=|P F|$, we know
$$
|| P F|-| P A||=|| P D|-| P A||=|A D|=6=2 a \text {. }
$$

Thus, the locus of point $P$ is a hyperbola with foci at $A$ and $F$, and $|A F|=2 c, 6<2 c \leqslant 12$, so $3<c \leqslant 6$, hence $e=\frac{2 c}{2 a}=\frac{c}{3} \in(1,2]$.
(2) When $F$ is on the line segment $A C$ (not coinciding with $C$), from $|P D|=|P F|$ we get
$$
|P F|+|P A|=|P D|+|P A|=|A D|=6=2 a .
$$

Thus, the locus of point $P$ is an ellipse with foci at $A$ and $F$, or a circle when $A$ and $F$ coincide. In summary, the range of the eccentricity of the hyperbola when the locus of $P$ is a hyperbola is (1, 2].
(Changqi No.2 High School Liu Anning provided the problem)
(7) Given that $C$ and $F$ are two points on line segment $AB$, $AB=12$, $AC=6$, $D$ is any point on the circle with center $A$ and radius $AC$, the perpendicular bisector of line segment $FD$ intersects line $AD$ at point $P$. If the locus of point $P$ is a hyperbola, then the range of the eccentricity of this hyperbola is $\qquad$.