They form a closed set under addition, subtraction or multiplication.
True.
Yes, no irrational numbers are whole numbers.
Different whole numbers are always whole numbers, but I suspect you meant to ask about the difference between whole numbers. You can subtract two whole numbers and get a negative result. Whole numbers can't be negative.
Atomic numbers are always whole numbers!
Yes, the difference of two whole numbers is always a whole number.
Yes, it is true.
True.
Whole numbers are always rational
Yes normally they produce whole numbers or integers
Always. By definition the Integers are the whole numbers; and the whole numbers are the integers.
No, integers are positive and negative whole numbers
No. 0 and negative integers are whole numbers but they are not counting numbers.