By law, the drinking age in Japan is 20. But as mentioned, it is almost never enforced. Keep in mind that there are still vending machines that serve alcohol in Japan, so it isn't all that hard to circumvent anyway.

The concept of counting age starting at 1 and adding another year to the count on Lunar New Year is based off of Chinese tradition and used to be widely followed in Sino-influenced cultures. See here for a detailed explanation. To keep it on topic with Japan, this practice has all but disappeared. Quite a few of my Japanese acquitances are completely unfamiliar with the concept.