One correction, or addendum, to Eric's list. "G" was for Great Lakes Aircraft Company. They were producing aircraft before Grumman hence they got the "G" and Grumman had to "settle for "F".
yes they did, using the Japanese calender year the Zero was Type '0' for the year 2600 (1940) the Val was Type 99 for the year 2599 (1939)...and so on...