I am reading the proof of the commutativity of intersection product from Ravi Vakil's notes: http://virtualmath1.stanford.edu/~vakil/245/245class8.pdf
This theorem states that if $D$ and $D'$ are Cartier divisors on an $n$-dimensional variety $X$, then $$ D \cdot [D'] = D' \cdot [D] $$
in $A_{n-2}(|D| \cap |D'|)$.
Question 1: On page 3, he defines $\epsilon(D, D')$. Why does it follow that $\epsilon(D, D')=0$ if and only if $D$ and $D'$ intersect properly (no codimension one variety is contained in $|D| \cap |D'|$)?
Question 2: On page 4, in the case when $D'$ is effective, why does it follow that $\pi^*D=C-E$, where $C$ is an effective Cartier divisor and $E$ is the effective divisor?