Anarchism is a great ideal, but implementing it would be incredibly stupid. Anarchism rests on the idea of voluntary trade between consenting parties for the benefit of both, and it relies on the idea that people are just and fair. People are not just or fair. There would be an incredible amount of crime and discord. The anarchist society would devolve into a group of warring factions.
Communism still generally has an authority figure though, be it a solitary figure or a group/council. In which case, communism becomes either a dictatorship or a democracy. Technically, the ideal of communism is anarchy.
Personally, I don't think it's possible to exist as a society without some form of government. I wish it was, but I just don't. The idea of "working together" doesn't seem possible, as most Humans are selfish bastards. It would probably last for a short while, before requiring a judiciary figure, leading to other authority figures - hence, government.
Also, for the record, I meant wouldn't anarchy become a form of democracy or face destruction or change into society with government. Potentially, you could run a democracy without a central government.
All of the above that you have listed can still be democratic, I think autocratoc would be a better description for what anarchy wouold achieve.
A monarchy for example can only be autocratic if it is absolute most monarchies are constitutional(side note; Lichtenstein & the Vatican are the only autocratic states left, whilst a few middle eastern countries are close to it namely Saudi Arabia).
If Anarchy if left to run its cause it would adventually turn to Autocracy where a self appointed ruler, most probably by force and influence, would seize the lack of power with their own power. This is why I prefer to use the word anarchy as meaning disorder, rather than a state without governance, as even with just two people on a desert island you will get an authority figure which in effect is governance.
Anarchism rests on the idea of voluntary trade between consenting parties for the benefit of both, and it relies on the idea that people are just and fair.