Which is fundamentally impossible. There are things that each of us cannot do due to our physical limitations - I'm too big and fat to be a chimney sweep, for example - and we should not be considered equally for those roles with people who are able to do them due to their physical limitations.
Sorry, I should have clarified what I was originally going on about. Originally when I was talking about equality I was referring to us all being given an equal opportunity to achieve our objectives. We can't often achieve what we want because of our own characteristics but we should all get the same opportunity to prove ourselves and no-one should get a head start because of wealth or something like that.
Who knows? I've seen (on CCTV!) a guy shove a sharpened biro into another guy's back 40 times just... because.
I doubt it was 'just because'. The guy will have had issues of some sort connected to either his home life or mental health problems. To go back to your point, most wars aren't just and are fought because of money and in the interests of very small number of people. In order to stop one person oppressing another then give no-one any power.
Just so we're clear, when you say "what we need is an abolition of private property" you mean that people should not be allowed to own... land? Buildings?
Either way, the second part remains - if they could [have possessions], anyone could take it from them by force because there is no protection from the use of force against them. You'll say that anarchy does away with rulers, not rules and the rules remain and I'll ask the question that, if there are no rulers, who enforces the rules?
If I collect records, what's to stop lots of people who are jealous of my record collection from forcibly removing it from me?
This is what Berkman said on the matter, "The revolution abolishes private ownership of the means of production and distribution, and with it goes capitalistic business. Personal possession remains only in the things you use. Thus, your watch is your own, but the watch factory belongs to the people. Land, machinery, and all other public utilities will be collective property, neither to be bought nor sold. Actual use will be considered the only title-not to ownership but to possession. The organization of the coal miners, for example, will be in charge of the coal mines, not as owners but as the operating agency. Similarly will the railroad brotherhoods run the railroads, and so on. Collective possession, cooperatively managed in the interests of the community, will take the place of personal ownership privately conducted for profit."
From that I presume that a house will be counted as a personal possession as long as you are using it, i.e. no second homes.
Your second point comes back to what I was talking about with the book, 'The Spirit Level - Why Equality is Better For Everyone'. Why would people commit crimes in a more equal society? Homicide rates are significantly lower in societies where wealth inequality is low. Also, trust is a lot higher in countries with a more equal distribution of wealth and why do people trust each other more in these societies? Inequality is a huge social divider, it separates people into 'haves and have nots' and you 'other' people that are not like you. There is also less conflict in more equal societies.
Self organisation is a way of preventing yourself from criminals. There is division in the anarchist community in this though. I assume though that you wish for a third party to become involved?
Why would people forcibly take your records? I don't believe that people are inherently bad.
Rules are enforced through a form coercion. The rules are agreed upon by direct democracy and so will no doubt be enforced by people collectively.