Yes.
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Integers are closed under subtraction, meaning that any subtraction problem with integers has a solution in the set of integers.
Yes.
1 No. 2 No. 3 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.
If you interpret "whole numbers" as "integers", then yes. If you interpret "whole numbers" as "non-negative integers", then no.