I think you've the wrong notion of equilibrium. There are equilibria in agent based models too (which are almost always DSGE models). Some have equilibria, some don't.
If some model has no equilibrium, then its dynamics are going to be determined exclusively by the assumptions you make about the agents. There's no "solution" to the model, so it's all in the dynamics. That's fine, but it's hard to learn anything from the chaos that ensues, since it's always determined by your assumptions. Or, at least, nobody has yet showed there's a lot to be learned from this.
If some model has an equilibrium, and it's not reached, then you need to explain why it's not reached. (Note you need some notion of equilibrium before you ask this question.) That's a very interesting question. We could learn a lot from that. Nobody has answered it in general.
I research network effects. There is a large literature on the subject. There is brilliant research being done on networks. It's not being done by Steve Keen. (Not really by me, either.)
What do you mean "disputes"? Nobody thinks that the assumptions required to reach an equilibrium can be, and regularly/almost always are, violated.
Ah here. Of course it does. It holds under the assumptions it requires.
Nobody does!
The dynamics of "any given point" to/from equilibrium is an enormous area of research. There are plenty of interesting results. Few of them are simple to explain, and none of them have permeated to undergrad texts yet. (As I said before in this thread, undergrads find equilibrium difficult enough. Trying to explain saddle paths/sink points/whatever would be a wasted venture.) Nobody is claiming that markets necessarily move toward equilibrium.