The "Zero Property" is actually called the Additive Identity Property. The additive identity is the unique number which, when added to any other number returns a sum which is the other number. 0 is the additive identity.
The Additive Inverse Property is that each nonzero number has a unique number which, when added to the number will return a sum of zero. (A more mathematical way to say this is that it will return a sum which is the additive identity.)
Examples: 23 + (-23) = 0 -(3/4) + (3/4) = 0 √3 +(-√3) = 0 - x2 + x2 = 0
The Commutative Property of Addition is that when two numbers are added together they will produce the same sum, regardless of the order of the two numbers.
Examples: 28.3 + (-12.7) = 15.6, -12.7 + 28.3 = 15.6
(1/3) + (3/4) = (13/12), (3/4) + (1/3) = (13/12)
What you are calling the 1 Property is the Multiplicative Property of Identity. It is not a property of addition. 1 is the identity for multiplication, just like 0 is the identity for addtion.