Proof of Proposition IV.3. 8 in Hartshorne Hartshorne book Proposition (IV.3. 8) is that

Let $X$ be a curve in $\mathbb{P}^3$, which is not contained in any plane.
   where, curve means a complete, nonsingular curve over algebraically closed field $k$.
  Suppose either
(a) every secant of $X$ is a multisecant. or 
(b) for any two points $P,Q$ in $X$, the tangent lines $L_P.L_Q$ are coplanar.
Then  there is a point $A$ in $\mathbb{P}^3$, which lies on every tangent line of $X$.

In proof,  fix a point $R$ in $X$, consider the projection from $R$ , $\phi:X-R \rightarrow \mathbb{P}^2$.
My question is that 
(1) If $\phi$ is inseparable, why the tangent line $L_P$ at $X$ passes through $R$ for any point $P$ in $X$?
(2) If $\phi$ is separable, does there exist point $T$ is a nonsingular point of $\phi(X)$ over which $\phi$ is not ramified?

For (2): In the separable case, the union of the singular locus and the ramification locus is a finite set of points.
