Congratulations on displaying an adequate high-school level of reading comprehension. I'm going to call that real progress!
I'd quibble with your restatement of the second point. The three fundamental points of disagreement I identified are not (necessarily) mutually-dependent, nor are any of them particularly consequential from any other. So your introduction of point 1 into point 2 is mistaken. I would better state my own contra-Rand view regarding that second point as something along the lines, "property
is a function of a context for enforcing exclusion". That context need not be government, and need not be monopoly -- it goes all the way down to "this stick is mine because it's in my closed (that is, not immediately accessible to anybody else) hand". We've got a lot of other, more nuanced modes of exclusion, but the principle remains that property -- contra Rand -- is not and cannot be an
a priori.
Similarly, your restatement of the third introduced two term that seems to add nothing of value over the one I had used, while at the same time subtly shifting the context (or so it seems to me) in a way that may cause us problems down the line. Strike your word "personhood" and use the one I did -- "Person". Then further on you make what appears to be a small shift, but which actually changes the idea drastically. That is, you turn "social context" into "social construct". The first is true, the second is not. To be correct, you would state the third point as something along the lines of: "Person only exists in a social context". I've analogized before that people are social creatures in the same way that fish are aquatic creatures.
I strongly suspect otherwise, but I'm more than willing to play along on the off chance that you actually have a coherent point this time. Bearing in mind, of course, the context of the current discussion -- you falsely claimed me among a number of "Randians" (along with the ludicrous assertion that I was somehow responsible for a particular parasite coming to wield political power!); I disputed that claim; you asked for three points of fundamental difference between my worldview and the Randian one; I provided, arbitrarily ordered, the first three that came to mind.