You said: “How can you have a social democracy that is anarchistic?”
You should check out my article An Intro to Anarchism. Anarchism, as defined by Proudhon, Bakunin, and Kropotkin—the founders of anarchism—was democratic. Sure, in some sense this is still government, but then so is the anarcho-capitalist model. Private police and private courts are still government, even if not monopolistic in form. Also, if people get together and voluntarily agree to follow a democratic process, is that really incompatible with anarchism as you define it?
I'll ignore your objection to defining capitalism as wage-slavery, since I have already answered it elsewhere (in the comments). But don't you think it's kind of authoritarian of you to dictate the meaning of the term? Most people have defined it differently than you have, and I showed that the people who coined the term defined it differently, but you insist that only your definition should be allowed.
You said: “... how do you incentivise good services without the concept of wages or capitalism?”
I never said abolish wages. I said abolish wage-slavery, the condition where people have no real viable alternative to wage labor. If people have access to land in order to grow crops, or to a basic income with which to purchase some means of production (tools and material to manufacture widgets at home, for instance), then they are freed from wage-slavery. Some people would still choose to work for wages, and that's fine, but no one would be forced to out of necessity.
You said: “You cannot have "free" anything, unless someone is willing to provide that good or service for no added benefit for themselves.”
That's basically a strawman. When social democrats talk about free services like universal healthcare, education, and such, we mean free at the point of service. Of course, we know that these must be paid for. As I said in this piece, land would be communally-owned and people would pay rent for private use of land, and such services would be paid with the money from that rent.
You said: “There already is a system of direct democracy. Its called free market capitalism.”
I have pointed out elsewhere (in the comments) that markets don't emerge in a vacuum, that government policy creates and maintains markets; where I cited Hayek, Graeber, and de Soto. Since you never responded to those arguments, I feel no obligation to reiterate or elaborate again, having already answered this objection.
You said: “So, how is that at all different from the county/state/federal solution we have today in the USA?”
Google “democratic confederalism,” “Murray Bookchin,” and “Abdullah Öcalan.” Such anarchist approaches to democracy are quite different from statist federalism. For instance, decisions would he made locally, directly by the people, with agreements reached at higher level being done through delegates (not representatives)—delegates who are bound by the democratic decisions made at the local level, who have no decision-making authority in themselves. The confederation would have no power to legislate or impose rules from the top down. The confederation, instead of being a top-down State, would be a mutual agreement, amongst various anarchist communities, for mutual assistance for defensive purposes. Also, the form of democracy would preferably be consensus-oriented in addition to being direct rather than representative in nature. Ideally, also, an anarchist system of direct democracy would be based on free association and confederation, so people would have the ability to opt out.
Now, what is interesting is that I can conceive of such a geo-mutualist society being established on a voluntary basis within an anarcho-capitalist system. Suppose that I am a billionaire. I buy several hundred acres of land. I could, then, create a society such as I described on my land. I can rent the land to others on the condition that the property and community of renters be managed on a directly democratic basis and that the rent be placed in a common treasury or account and be used for maintenance of roads, buildings, etc; that a doctor be hired for the community, being paid out of the rent money, and visits and treatment will be free at point of service, having already been paid for in the form of a mixture of mutual insurance and lodge practice arrangements; and I can also make it a condition within the rental agreement that any excess rent revenue, which is not used for maintenance or insurance/doctor costs, go back to all the renters in equal shares. Such a geo-mutualist society, within an anarcho-capitalist framework, would be totally voluntary according to anarcho-capitalist principles.
You said: “Land ownership,” etc. etc.
On this, I direct you once more to my Steemit series Property as Theft: The Libertarian Socialist Critique of Property. But also, I reiterate that this geo-mutualist society could be established upon anarcho-capitalist principles. If I remember correctly, Fred Foldvary has even made such a proposal, to establish voluntary Georgist or geo-anarchist communities as private communities within a more or less anarcho-capitalist system.
RE: On Anarchist Social Democracy: Taxation, Welfare, and Anarchy