Как да групирате по месеци и да върнете нула, ако няма стойност за определен месец?

Направете таблица с всички месеци и след това left join на вашата маса:

SELECT MONTHNAME(m.month) AS mName, 
    MONTH(m.month) AS mOrder, 
    ifnull(sum(amount),0) AS total_num 
from months m
left join income i
on m.month = i.date

GROUP BY mOrder 
ORDER BY mOrder DESC

Ако не искате да създавате months таблица, тогава можете:

(select STR_TO_DATE('01/01/2016', '%d/%m/%Y') as month union 
 select STR_TO_DATE('01/02/2016', '%d/%m/%Y') as month union 
 select STR_TO_DATE('01/03/2016', '%d/%m/%Y') as month union 
 select STR_TO_DATE('01/04/2016', '%d/%m/%Y') as month union 
 select STR_TO_DATE('01/05/2016', '%d/%m/%Y') as month union 
 select STR_TO_DATE('01/06/2016', '%d/%m/%Y') as month union 
 select STR_TO_DATE('01/07/2016', '%d/%m/%Y') as month union 
 select STR_TO_DATE('01/08/2016', '%d/%m/%Y') as month union 
 select STR_TO_DATE('01/09/2016', '%d/%m/%Y') as month union 
 select STR_TO_DATE('01/10/2016', '%d/%m/%Y') as month union 
 select STR_TO_DATE('01/11/2016', '%d/%m/%Y') as month union 
 select STR_TO_DATE('01/12/2016', '%d/%m/%Y') as month)