Lets say we have something like:
SELECT COUNT(IF(Column1 = 1, NULL, 1)) AS "A", SUM(Column2) AS "B" FROM MyDatabase;
On the same query, can we add a column that would be A * B for example with one single SELECT overall?
You need to either repeat the expression, or turn it to a subquery and do the computation in the outer query. Your expression is not that complicated (and can be simplified, as shown below), so I would go for the first option here:
SELECT
SUM(Column1 = 1) a,
SUM(Column2) b,
SUM(Column1 = 1) * SUM(Column2) c
FROM MyDatabase;