There is only one set and it does have an additive identity.
Yes. The additive identity is 0.
I t is the number 0, which has the property that x + 0 = 0 + x = x for all rational numbers x.
Yes: it is 0.
Zero is the additive identity in the set of real numbers; when you add zero to any number, the number does not change its identity.
Yes, it does.
Wrong! Not only is zero a real number, but it is the additive identity for the set of integers, rational numbers as well as real numbers.
No. It has a different additive inverses for each element.
Yes. The multiplicative identity for the rational numbers is 1 (also can be written as 1/1).
Yes, it is 1.
0 is the additive identity for the set of numbers.