Private property will not exist under anarchism, since private property (read the means of production) will be placed into the collective hands of those who need it.
anarchy (which ultimately leads to individualism and capitalism)
Capitalism requires the maintenance of involuntary hierarchies (like that between the owner and worker) and thus is antithetical to anarchism.
I believe anarchy and communism are polar opposites,
The ultimate goal of communism is the dissolution of state, this is something even MLs agree on.
"Engels suggested to Bebel that all chatter about the state be dropped altogether, that the word “state” be eliminated from the programme altogether and the word “community” substituted for it. Engels even declared that the Commune was long a state in the proper sense of the word. Yet Marx even spoke of the “future state in communist society”, i.e., he would seem to recognize the need for the state even under communism.
But such a view would be fundamentally wrong. A closer examination shows that Marx’s and Engels’ views on the state and its withering away were completely identical, and that Marx’s expression quoted above refers to the state in the process of withering away."
If you wouldn’t mind me making an assumption, it appears that you have very little knowledge of anarchism’s philosophical framework. I can give you some reading suggestions if you’d like.