elf:
What kind of sensors could I use to determine if two plates were parallel to each other and secondarily the distance and angle between the center points of each plate?
If your intention is to move/control the platform with steppers, I would not look for sensors, but rather base it on a model of the platform dynamics. Positional accuracy and awareness would then be limited only by stepper angle resolution. Working out the math is not trivial, but then again this would be a core challenge and most likley a requirement of such a project.
If you need to relate the platform to life coordinates (gravity) then a 3D accelerator could be used. They typically have a 12-bit resolution across 180 degrees (approximately 0.1 degree).