No.
1 + 3 = 4, which is not odd. In fact, no pair of odds sums to an odd. So the set is not closed under addition.
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Yes
Yes they are closed under multiplication, addition, and subtraction.
Rational numbers are closed under addition, subtraction, multiplication. They are not closed under division, since you can't divide by zero. However, rational numbers excluding the zero are closed under division.
Yes.
If you mean the set of non-negative integers ("whole numbers" is a bit ambiguous in this sense), it is closed under addition and multiplication. If you mean "integers", the set is closed under addition, subtraction, multiplication.