I am reading Chapter 3 of the book "Singularities of the minimal model program", and I have some problems on calculating certain quantities.

Let $X$ be a projective variety, $L$ be an ample line bundle on $X$, and $K_X \sim_{\mathbb{Q}} rL$ for some $r\in \mathbb{Q}$. Then one can define the affine cone ($\S$ 3.8 loc. cit)

$$C_a(X,L):={\rm Spec}_k\sum_{m \geq 0}H^0(X, L^m),$$ and its partial resolution

$$p: BC_a(X,L):= Spec_X\sum_{m \geq 0}L^m \to C_a(X,L).$$

Let $E$ be the exceptional divisor of $p$, and $\pi: BC_a(X,L) \to X$ be the $\mathbb A^1$-bundle which identifies $E$ with $X$.

My problems are the following (it appears in Proposition 3.14, loc. cit):

(1) Why $\mathcal{O}_{BC_a(X,L)}(E)|_E = L^{-1}$?

(2) Why $\pi^*(K_X) \sim_{\mathbb Q}-rE$?

The (2) is especially confusing me: suppose $r>0$, then $K_X$ is ample, how come $\pi^*(K_X)$ is not effective (i.e.$\sim_{\mathbb Q}-rE$)?