I totally agree with you on agreeing on definitions and terms. I also have had the experience of arguing at cross purposes because of a difference in accepted terminology. (ex. fascism, capitalism, corporatism, etc). As I'm reading through your response several terms and items jump out at me.

"There are no serious leftists advocating for confiscating handtools, computers, furniture, or other such pieces of individual property from the entire population and redistributing them equally. Although the definition can be construed this way, no one is arguing for that. "

I would have to contest this point. Does it matter if you demand that a man turn over a loaf of bread if you put in place food rationing or tax the price of that loaf of bread? Does it matter if a man has a his physical assets left alone if his liquid assets are limited or taken from him? I find it ironic that the left labels hiring someone as exploitation but denies that taxation is extortion. The same with denouncing economic monopolies but promoting government which is a monopoly on violence by definition. If power is to be distributed then everyone should be responsible for their own self defense and monopolies on violence should be dissolved with the same vigilance as economic monopolies. Where is the antitrust agency against governments?

"Private property, as the antithesis to social, collective property, exists only where the means of labour and the external conditions of labour belong to private individuals. "

What? Labor = private individuals. He who creates owns. He who labors trades. This is why I find Marxism confusing. You don't get capital without mixing your labor with resources. You can't trade for some other product without gaining some kind of capital. Laborers = capitalists. Capitalists are not some upper class rich folks. If you plant seeds, till the ground and reap a harvest then that harvest you yield is your capital. if you sell that food you are a capitalist even if you are only making enough to keep your home running and to plant next years crop. Trade = capitalism. This whole paragraph makes NO sense! I'm just going to say that up front.

"From that moment new forces and new passions spring up in the bosom of society; but the old social organisation fetters them and keeps them down. It must be annihilated; it is annihilated. Its annihilation, the transformation of the individualised and scattered means of production into socially concentrated ones, of the pigmy property of the many into the huge property of the few, the expropriation of the great mass of the people from the soil, from the means of subsistence, and from the means of labour, this fearful and painful expropriation of the mass of the people forms the prelude to the history of capital…"

First of all centralization of wealth didn't just happen organically. Corporate charters are a product of the state. So is colonization. Seriously where would Big Pharma or Big Media be without patants and copyright? Where would modern economics be without limited liability? What if we stopped backing corporations up with government protectionism? "That guy copied my drug formula!" "That guy won't stop making free copies of my music album!" "That business copied my logo!" " Help I'm being sued for making a dangerous product and useless warning labels!" Don't get me started on private banks, the federal reserve or the IMF etc, all of which are ALSO businesses backed by government. Governments didn't just magically get money and land either. They literally stole it from other people for the most part through force of arms. So when you take monopolies on violence out of the picture and government protectionism out of the picture what are you left with? Self owned businesses backed by labor and trade, ie what Marx would call "laborers". Granted there can be centralizations of wealth but this can be countered by people just copying, innovating and undercutting others.

"Self-earned private property, that is based, so to say, on the fusing together of the isolated, independent labouring individual with the conditions of his labour, is supplanted by capitalistic private property, which rests on exploitation of the nominally free labour of others, i.e., on wage labour…"

Yeah this is another what? How is hiring and PAYING THEM free labor? You're out the cost of their pay cheque! They are literally trading their time and effort for money. How is that free labor either way? Moreover how is that exploitative? One could argue that one CAN exploit others by underpaying them but that's not what is being discussed here from what I understand. This seems to be a general statement about employment. So yeah, what?!?! Definitely a difference in terminology there.

"The capitalist mode of appropriation, the result of the capitalist mode of production, produces capitalist private property. This is the first negation of individual private property, as founded on the labour of the proprietor. "

As explained before there is no "capitalist" vs "individual" private property. The individual IS a capitalist. Ergo there is just "private property." Much of this seems to be discussing class divisions but trying to create a difference in terms between those who trade in goods and services and those who produce those goods and services. To use an example. A farmer grows a crop. He then sells that crop to a traveling merchant caravan. The caravan then transports those food stuffs to a big town market where they are resold by grocers in the marketplace. When does one start being an elite? Is it the caravan owner? The marketplace vendors? Who?

"But capitalist production begets, with the inexorability of a law of Nature, its own negation. It is the negation of negation. This does not re-establish private property for the producer, but gives him individual property based on the acquisition of the capitalist era: i.e., on cooperation and the possession in common of the land and of the means of production. (Chapter 32)"

You're going to have to explain that because that makes zero sense. None. Zip.