Will heavy mining eventually deplete a node completely? What do we do to stop somebody from just posting up somewhere and staying on it forever?

So yes, it will deplete it completely. Yes, we want that. We want the nodes to get depleted, or even destroyed if you're not mining them accordingly. They will become harder and harder to mine the lower the quantity of material inside is, and then the population of mineable objects will get replenished over time.

And we'll have to figure out how that happens as well. That'll be one of the things that we try to work out in Tier 0, Tier 1: how these things get replenished.