A Right Angle at the Top Vertex

In the plane, the ellipse $C: \dfrac{x^2}{3} + y^2 = 1$ has top vertex $A$. A line $\ell$ not through $A$ meets $C$ at $P$ and $Q$ with $\overrightarrow{AP} \cdot \overrightarrow{AQ} = 0$.

1. Does $\ell$ pass through a fixed point? Find it or explain why not. 2. The tangents to $C$ at $P$ and $Q$ meet at $B$. Find the range of the area of $\triangle BPQ$.