Why is acetylsalicylic acid still more acid than benzoic acid?
The acetyl moiety in acetylsalicylic acid has a $(-I)$-effect, i.e. compared to a proton attached to the aromatic ring (as in the case of benzoic acid), it withdraws electron density out of the aromatic ring.  This provides an additional stabilization of the conjugated base, that is equivalent with rendering acetylsalicylic acid a stronger Brønsted acid than benzoic acid.  Hence, the $pK_a$ of acetylsalicylic acid is lower than the one of benzoic acid.

Regarding the second paragraph, please notice $pK_a$ is a thermodynamic property -- where time does not play a role.  In contrast, the substitution reactivity you likely refer to (Hammett parameters) refers to reaction kinetics and rate constants.  Here, time does play a role.