Are there size classes for fighters like there are for weapons? Like, will I ever be able to dock another similarly sized fighter to a constellation? Or is that docking mechanism specifically designed for only the Merlin/Archimedes?

The collar on the back of the Constellation is designed specifically for the Merlin/Archimedes. It could be possible in the future that other collar options could be available, but that would be a long ways out and would need a healthy range of Snub-ship options to really support it.