Is installing electrical & plumbing in a Monolithic Dome different?

For plumbing, there is no difference. All homes, including domes, run sewer and water pipes in the interior walls of the home. There is no reason to penetrate the dome wall other than for a garden hose connection and vents.

Electrical wiring requires a little more planning and preparation before constructing your dome. Plan where you want electrical outlets and lights in the dome wall. During construction of the dome, attach plastic or steel conduit to the rebar. Also fasten the electrical boxes in the appropriate places. After the concrete is sprayed, wires may be pulled through the embedded conduits to their appropriate boxes.