I realize that נכסים here is a plural noun, but does it necessarily refer to more than one item? In English, if I were pointing to land that belonged to me, I would say "this is my property." Would you say "זה הנכס שלי" in Hebrew?
You can refer to a house or a piece of land as הנכס שלי. But if you want to talk about all your belongings, you'd use the plural form.
If you are trying to say "all my properties ate this one", you might use plural when referring to a single object. Otherwise, it is plural like any other noun.
"These properties are mine", was not accepted?
Because it is different. That would be הנכסים האלה שלי
The word נכס is related to Aramaic נכסין and Syriac ܢܟܤܐ, via Akkadian nikassu (source: Kaufman, Akkadian Influences on Aramaic, 77). Probably also Arabic خاصية (khaasia) is also cognate.