Which of the following statement(s) is/are correct?

(A) The pH of $1 \times 10^{-8}$ M HCl solution is 8.
(B) The conjugate base of H$_2$PO$_4^-$ is HPO$_4^{2-}$.
(C) $K_w$ increases with increase in temperature.
(D) When a solution of a weak monoprotic acid is titrated against a strong base at half neutralisation point, pH = $\frac{1}{2}$p$K_a$.