While it might make more logical sense to have separate passageways for air and food/water, this did not happen in evolutionary history due to the peculiarities of lung development. Vertebrate lungs develop as an outpouching of the gut tube, which itself has a very long evolutionary history (probably homologous among all deuterostomes).
In the image below, the trachea has budded off the esophagus. Further lung development will involve the differentiation of main, secondary, and tertiary bronchi as well as the alveoli, etc.
Additional images and description at http://www.uoguelph.ca/zoology/devobio/210labs/lung1.html
Air-filled organs like lungs and swim bladders actually have a broad distribution going way down into fishes. Human (and other mammalian) lungs are likely homologous with ancestral air-filled organs of fishes. We can't be certain, but there is no reason to think that mammalian lungs are a de novo evolutionary innovation. So our airway and food-ways are tied together developmentally and are constrained by evolutionary history.
As for breathing and eating (swallowing) at the same time, most mammals can do this, and baby humans can as well.
Like most anatomical systems that seem as though they could have evolved better, this system works most of the time and has worked well enough for hundreds of millions of years.