That's not true. All sets have zero or more elements. You can have a set with zero elements - the "empty set".
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It is a mapping. The information provided is not sufficient to determine if it is a function, an inverse function or neither.
Two sets are equal if they have the same elements. Two sets are equivalent if there is a bijection from one set to the other. that is, each element of one set can be mapped, one-to-one, onto elements of the second set.
An element in the set A or B is one that is in the union of the two sets. It can be in A or B or both.
It is the multiplicative identity of numbers in most sets. It can also mean the "most important" element or member.
It is the multiplicative identity of numbers in most sets. It can also mean the "most important" element or member.