Yes, it does.
No. It has a different additive inverses for each element.
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.
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 is not.
Yes: it is 0.
The set of rational numbers includes the set of natural numbers but they are not the same. All natural numbers are rational, not all rational numbers are natural.
Yes - the set of integers is a subset of the set of rational numbers.
The Real numbers