A Median of Length One

In $\triangle ABC$, the sides opposite the angles $A,B,C$ are $a,b,c$. The area of $\triangle ABC$ is $\sqrt 3$, $D$ is the midpoint of $BC$, and $AD=1$.

1. If $\angle ADC=\dfrac{\pi}3$, find $\tan B$. 2. If $b^2+c^2=8$, find $b$ and $c$.