0 always has been and always will be a completely valid member of the Real numbers. (The numbers that can describe physical quantities)
it's not a multiple of two because you can multiply by 0 and get anything other than zero.
This is incorrect, the definition of an even number is that it's divisible by 2, that x / 2 is a whole number and not a fraction or irrational number. Another way to put it is that if x mod 2 = 0 then x is even.
Both of those hold true for 0: 0/2 = 0, which is a whole number and has no fractional part. 0 mod 2 = 0 as well. Therefore, 0 is even.