If anarchists are true to their principles, then yes, they are necessarily against all government. This does not mean that they might not choose to live by certain social mores. What is different is the formality of structure. Whereas anarchists might choose to live by common agreements, or even to operate within groups which use democratic decision making, those ties are hardly enforced through law. There might be social stigma, shunning, or rejection from groups (or further, violent retribution or reaction) based upon the individual’s choice not to participate in such mores, but ultimately, if I choose to not live by the commonly held standards, it is my right. This opens up lots of other cans of worms, but that is likely another question and one that I might endeavor to explore, but wouldn’t pretend to have the answer to.
Anarchists who speak of direct democracy are, in my opinion, doing themselves and anarchism/y a disservice. Using the terminology of democracy seems to have come into vogue with Murray Bookchin and his adoration of the ancient Greek city-state as well as the New England Town Hall, and really caught hold following 1999 WTO protests plastered the chant of “This is what democracy looks like,” into the public consciousness. It was at this point that I started to take note of lots of anarchists (in particular social ecology types and some anarcho-syndicalists) propagandizing anarchism as a sort of ultra-democracy: the most democratic of all democracies. Ultimately though, even direct democracy means the individual bows to the decision of the majority, and, if formalized (even if done face to face as opposed to through representation) this is decidedly not anarchistic.
Regarding consensus, it does, ideally, ensure that all voices are heard, and that a mutually beneficial and acceptable course of action is taken. I am a fan of consensus, but I also think it can be easily manipulated and abused, and have always understood consensus to work in an anarchistic (I HATE that word) manner if the group making decisions is both solid enough to be able to find common means and ends, and fluid enough that people are free to pick and choose when a decision will affect them.
The difference, to riff off of what Enkidu wrote, between “government” and “self governance” is that one is imposed upon by threat of external coercion, and one is internal. This doesn’t begin to address the problem of eliminating our internal cops, spooks, and so forth, but it is an important distinction, all the same.