No problem using a common power supply that I can imagine.
I would NOT try to use a single capacitor, you want the cap directly across the relay coil, and the switching of the DC to be after the current limiting resistor.
I don't understand the third question. One side of either relay is to the positive output of the power supply (bridge rectifier), and the negative is supplied by the isolated track section. The negative output of the bridge rectifier goes to the track power common. So, when a train rolls onto the isolated section, the common is connected to the isolated rail and charges the cap and closes the relay. When the train leaves the isolated section, the cap discharges through the relay and then the relay opens after the discharge delay.
