The はよう one is more interesting and complicated. You probably still won't understand that one after reading Tae Kim's guide. :P
JCJP doesn't teach grammar, however it does like to try to expose you to a vast variety of different and obscure grammatical constructions. ^^
Normally 早う (はよう) would be seen as 早く (はやく). はやく is the adverb form conjugation of the adjective はやい. The はよう version is the result of historical sound changes. Also, はよう would be はやう but spelling reform affected the spelling of "~a + u" sound to be rewritten as "~o + u".
November 2, 2014 at 4:14am