Definitely possible (they could use the Bitmessage protocol, for instance) - but not worth the bother. Reliable P2P C&C channels already exist and are widely used.
With all due respect, this makes no sense. Lay off the SciFi, why don't you.
Somebody did that recently. They made a full simulation of a nematode (a small worm, 1.2mm long), down to every cell and every neuron connection (some 600+ of such connections). Then they let it "roam" in a simulated environment and it behaved exactly like the real thing.
Simply unnecessary. There is no need for the botnet to have such a memory and intelligence; it unnecessarily complicate things without added survival. All that is needed is for the bot herder to learn about the attacks and relay his commands reliably to the botnet - and we have that already; using a blockchain adds no benefits.