Who wrote "Fishhawk" and "Plums are falling" (Chinese classic poems)?
Unfortunately, after a brief internet search, I can't find any indication of a poet's name being associated with either of these poems. Because they are both so old and represent two of the finest examples of Chinese classical poetry, unfortunately they are two poems that we do not have any idea of who the author is. No website gives any indication at all as to their origin or who might have written them.
However, what is clear is that these two poems do represent Chinese classical poetry as an emerging form in its finest and most exquisite sense, and it is for this that these two poems are extolled today and studied so much. Even though we do not know who wrote them, that still does not mean that they are not of literary merit. I have included some links below to more information on Chinese poetry which I hope you find useful.