You have the right idea for the mechanism, but you protonated the wrong oxygen. In an ester, the carbonyl oxygen is much more basic because the resulting cation can be stabilized by resonance, whereas the structure you drew cannot be stabilized by resonance. Once you protonate the carbonyl oxygen, MeOH attacks (as Dan said, it's not MeO-) to form a tetrahedral intermediate. After that, you would transfer the hydrogen that came along with the MeOH to the other ether oxygen (the oxygen you showed as protonated) and then collapse the electrons from the OH group to make a carbonyl and release the alcohol.
As for the combination of reagents, MeOH/AcCl, this is a common way to generate dry HCl in solution. Otherwise you would have to use HCl gas. Aqueous HCl can't be used because it would hydrolyze your methyl ester to the carboxylic acid with water in the pot.