Division and subtraction cannot be used with the commutative property.
Addition & multiplication
Try it out. 3 + 9 = 9 + 3 That works. 3 x 9 = 9 x 3 That works. 3 - 9 = 9 - 3 That doesn't work. 3/9 = 9/3 That doesn't work. The numbers came first. The commutative law was only devised because of the relationship of the numbers. It isn't that the commutative property doesn't work for other operations, it's that the other operations aren't commutative.
addition and multiplication
Commutativity is a property of binary operations. A fact is not a binary operator.
No, it does not.
Yes. The additive identity is always commutative - even in sets with binary operations that are not otherwise commutative.
Not sure what "would not work" in this case. The corresponding commutative property states that 5x4 is the same as 4x5.
Addition and multiplication are operations on integers that are commutative.