On the issue od the NAP, I think it's error does seem to, to more clearly state it, starts from a poor primise of not being agressed on.
It implicitly buys into the rosouian idea of people being born free and everywhere in chains.
This is not the case. As we've acknowledged, NAP doesn't apply to children. You are born dependent, in bondage, to your parents. So, at basic, NAP doesn't apply for, what, the first 15? 20? 30 years of life?
Everyone is born in chains, and with 20-40 years of hard work, may earn freedom. Thats how long it takes of aggression to force the NAP into someone.
Likewise, the only way to have a meaningful NAP is to agress against everyone who is not a libertarian until they yield to the principle.
The "libertarians want to take over the world to leave you alone" is a joke, but has the grain of truth that imposing libertarianism would require wielding an immense amount of aggression against, well, a majority of people.
As to an earlier discussion, of course communists push liberty. Look at any of their rhetoric, and how many organizations were call x liberation y. The communist subversion of Catholicism is literally called liberation theology.
Liberty and freedom are core parts of the rhetoric of communism. That they don't generally provise that, or provide a form of liberty that libertarians like, is immaterial to the discussion.