555 Charge Controller Schematic Explanation
Yes, your three external devices (12V Battery, Wind/Solar, Dummy Load) are meant to have their second terminal connected to the common ground. And yes, all the ground symbols in a schematic are meant to be connected, too.

The relay inductor gets its power from the Battery/Wind/solar, as the rest of the circuit does. Maybe you are confused because it's the part where the two "big loops" (inner circuit, external parts) share a path?