That distribution doesn't have to be top down. And as communism is a stateless society, the entire concept is predicated on the absence of top down distribution. Read up on democratic confederalism, parecon, project cybersin (admittedly done with the presence of a state but there's nothing about the system the necessitates one).

The CNT-FAI, zapatistas, rojava, and free territories of ukraine can all speak to decentralized militias. For auth-left examples just check out maoist militant orgs, they drew a ton of inspiration for anarchists in how to manage militias.

Most anarchists are prison abolitionists, I'm not going to summarize that one, look into it if you wish

Market economies can and have existed in horizontal societies. There's nothing inherently contradictory regarding trade regulations in a horizontal society