> Can the true statement have multiple operations listed?
You mean you want the displayed result to show a list of the comparisons that went into it? You could write out the conditions as a matrix of 1 and 0s ...
select
aquaculture_id,
year_a,
species_code_a,
qty_prod,
if( qty_prod=0, 1, 0 ) as 'zero',
if( qty_prod < (0.5*max_prod_5, 1, 0 ) as '< 50% 5yr avg',
if( qty_prod between avg_prod_5 and avg_prod_1, 1, 0 ) as 'in 5-10 yr range',
if( qty_prod >= avg_prod_10 and area_change_a > 0, 1, 0 ) as '>10 yr avg',
if( area_change_a < 0, -1, if( area_change=0, 0, 1 ) as 'area_change'
from fao_aquaculture;
... then combine & describe them as desired in an outer query.