You can't distill out pure methanol, as at the boiling point of methanol ethanol also has some vapor pressure, so you distill a mix. However above that boiling point you distilled out all methanol (with a mix of ethanol), and the remaining ethanol should be free from methanol.

This also matches what happens when distilling ethanol from water. You can't distill pure ethanol, but you csn distill ethanol-free water afterwards.

Yup, distillation never produces a pure product. Cask-strength whiskeys contain quite a lot of water, even though nobody is stupid enough to distill at 100C. Even an industrial column still can't go over 96% ABV.

There is always some amount of vapor pressure, even below the boiling point of a substance. Otherwise, neither water nor alcohol would evaporate by themselves at room temperature! The temperature we call the "boiling point" is just the temperature at which the vapor pressure equals the ambient pressure.