There are a few different points within this that are, to my mind, distinct. I will address them each in turn.
If the goal of class war is destruction or leveling of class-based society altogether, then sure, one could say that class war is a form of classicide (the total elimination of classes). As class struggle anarchists speak of it, it generally manifests as a hatred of the bourgeoisie and the rich, and the resulting acts against them (presumably these class struggle anarchists are either from the working class or reject the class privilege that they have). I don't really identify with the whole class war tendency, so I expect that I will either have mischaracterized parts, or that there is more to say about this.
What I can say more certainly is that the anarchists I consider friends don't want a proletarian dictatorship. I personally am more interested in the destruction of "work" as a distinct aspect of life, but excepting that, communes, and workers' councils, as anarchists use the terms, are not the same a dictatorship of the proletariat or a singular ruling party.
Most current (North American) anarchists who use the term commune (and I don't generally) mean something different than a distinct communal farm, workplace, etc (those could be communes, but they are not the only communes - to my mind, it is almost like the verb commune is what is being used, as opposed to the noun).
Workers' councils, in anarchist parlance, are bodies for making decisions within the framework of a workplace, and of a network or federation of workplaces. They are not organs for a party, as some authoritarian communists might use the term, as there is no central political group making decisions or planning the course of things.
As to the complete suppression of the bourgeoisie, it really depends what you mean. Again, if all class structure is eliminated, it would follow that the bourgeoisie wouldn't exist any longer. If concepts such as property and capital no longer hold water, then the things that make them bourgeois will be gone. As far a suppressing their reemergence, it sort of depends which anarchist you talk to what their ideas around that would be. Personally, I figure some reeducation camps Pol Pot style would be best (kidding, with a nod to some of the most fallacious accusations thrown at anti-civ types).
To answer your last question - I think we have to. Anarchists as a self-identifying group of people have never been and will likely never be the majority. It isn't necessary for that to be the case for anarchy to occur. Actually, most of the anarchic moments in my life happen when I am with friends (many of whom are not Anarchists).
This actually points out a problem I had in trying to answer this - it is looking to a future (theoretical) configuring of society, as opposed to a way of acting right now. Where we are right now is not some ideal world, and I don't believe that someday the anarchists will have a precise moment of revolution where suddenly the old world is gone and we are ushering in a new anarchist one. I think it is about finding and expanding the places that already exists, while also opening up new spaces for anarchy to happen.