I know you can start a chain during the draw phase. But what about your Resource phase?

Can I put a resource down, flip it, and use its ability while still in the resource phase?

Pretty much. You have to play a resource (or choose not to) at the start of the step before anyone gets priority. You are allowed to play any effects after that point, though, since you have a priority point there before the recruit step.

So you can't do stuff before you place the resource?
I thought I was being clever using draw effects like birthing chamber to get something useful to put in my resource row. Now it seems I have been misplaying...oops:o

Well, you do have the start of the build phase as well as the draw phase to do it. The only proviso is that the cost has to be low enough to play before setting the turn's resource.