Let $S$ be a normal (complex) projective surface with quotient singularities (locally analytically isomorphic to $\Bbb C^2/G$ where $G\subset \text{GL}(2,\Bbb C)$ is a finite group whose action is fixed point free outside the origin). Let $f:S'\to S$ be the minimal resolution. I am looking for a proof or reference of the following facts:
Quotient singularities are log-terminal singularities, so we can write $K_{S'}=f^*K_S -\sum D_p$, where $D_p=\sum (a_jE_j)$ is an effective $\Bbb Q$-divisor supported on $f^{-1}(p)=\cup E_j$ and $0\leq a_j <1$.
Quotient singularities are rational, so $p_g(S')=q(S')=0$.
Actually I am reading this paper: https://arxiv.org/pdf/0801.3021.pdf. Fact 1 is given in the last paragraph of p.6, and it is written that it is well-known. Fact 2 is given in the proof of Corollary 3.4, p.8. Is there a reference to find proofs of these? Thanks in advance.