No, most cannot.
No, they cannot.
Positive integers, if I understood you correctly
bytes integers long integers short integers word double word strings
addition
Yes it is : a + b = b + a for all integers a and b. In fact , if an operation is called addition you can bet that it is commutative. It would be perverse to call an non-commutative operation addition.
yes
Yes.
1) addition
The answer depends on what the operation is.
add subtract divide multiplication
No. It is not a group.
There are no consecutive integers that add or multiply to 224. If you meant some other binary operation, you should specify what you meant.