>Communism is total government, Anarchism is no government. Its oil and water.
This is false. Communism leads to a stateless society, which is known as anarchism, i.e without rulers. Where do you get your information that Communism has a government?
> each person works and is paid according to their abilities and needs.
Wrong! Workers are not paid within Communism, they collectively own the means of production and decide what to do with the products. Payment is a form of wage, and Communism abolishes wage labour completely. Communism is also moneyless.
"All Socialists are agreed that the political state, and with it political authority, will disappear as a result of the coming social revolution, that is, that public functions will lose their political character and will be transformed into the simple administrative functions of watching over the true interests of society."
-- Freidrich Engels, one of the founders of Marxism (https://www.marxists.org/archive/marx/works/1872/10/authorit...)
>If there is no government, who distributes things based on needs?
The workers collectively decide in the form of democratic voluntary participation councils whether anything should be distributed, to whom it will be distributed, how much is produced, etc; ideally these would be distributed, and several such councils exist all connected to each other, but none with authority over the other. In Communism, goods are not necessarily distributed, the workers receive the goods. However with the state of automation and abundance of resources (all resources are accessible collectively by the workers) sufficient can be produced to sustain others. However again, this is the collective and democratic choice of the workers. The kind of democracy I am talking about is not representative, it is direct or delegatory, and if delegatory the delegates are subject to instant recall.
>Why don't I just kill you and take everything you own?
Why would you steal in a society in which you yourself, a worker, collectively own the automation and tools to make what you want for yourself? Of all the offences, why would you choose theft? Within anarchism, how to deal with a violent offender would probably be a democratic decision. If you're interested in the crime question (which is a little problematic because 'crime' is defined by the state) then here is some reading:
https://theanarchistlibrary.org/library/scott-of-the-insurge...
https://theanarchistlibrary.org/library/robert-anton-wilson-...
http://anarchy101.org/2784/would-anarchist-society-with-crim...
https://www.reddit.com/r/DebateAnarchism/comments/44n3zi/how...
https://www.reddit.com/r/DebateAnarchism/comments/3uhbfv/how...
https://www.reddit.com/r/Anarchy101/comments/2ph8uw/how_woul...