Do stations need raw materials in order to produce items, or do they always have an unlimited supply of whatever they are set to produce? And similarly, do stations resell the goods that they buy or do they only sell items that they are set to produce? If nobody ever mines any ore, will station supplies of ships and weapons eventually dry up?

As of right now all stations have unlimited supplies of everything.

There is however a discussion thread started by Incarnate for a Crafting/Production system.

http://www.vendetta-online.com/x/msgboard/3/11406

We're still working on getting some of the automated infrastructure (like bots mining things and delivering them) reliable enough to where we can consider doing stuff like this. That's part of the "Kourier" project that's been going on this year. Kourier is more or less a "bot control and oversight" mechanism, which applies to everything from the Hive to automated trading convoys and the like.