Given the ellipse equation $C : \frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1 ( a > b > 0 )$. The foci and endpoints of the minor axis form a square with side length 2. A line $l$ passing through $( 0 , t ) ( t > \sqrt { 2 })$ intersects the ellipse at points $A, B$, and $C ( 0,1 )$. Connect $AC$ and it intersects the ellipse at $D$.\\
(1) Find the equation of the ellipse and its eccentricity;\\
(2) If the slope of line $BD$ is 0, find $t$.