In general, can I substitute egg species for either egg-only or egg-centric dishes?
More or less, yes. Just know that eggs of different species have different "flavors." There may be some issues with substituting in dishes due to varying fat content of the yolks and such...

I've had duck and goose egg quiches. I've had fried quail eggs on toast. I have yet to try an ostrich or emu egg.