question on finite Blaschke product and its Julia set

Question

I would like to make my previous question more precise.

1. If $B$ is a finite Blaschke product such that its Julia set $J_B$ is a Cantor subset of $S^1$, then is it true that $B$ is expanding on $J_B\,$?

2. If $B$ has a parabolic fixed point on $S^1$, and $J_B = S^1$, then is it true that $|B^\prime| \geq 1$ on $S^1\,$?