Electrical – Are the plans for adding a 240 volt circuit reasonable

If you're in the United States, a grounding conductor is defiantly required for all new work.

If the system was installed before grounding was required, you're not required to update the system and add grounding when the code changes. However, if you add anything to the system after the code change, you must do so in a code compliant manner. This might mean bringing the entire system up to current codes, or at least enough of it to allow the new work to be code compliant.

You might be able to simply install a proper grounding electrode at the building, and use that to ground the circuits on the secondary side of the transformer. You'll have to contact your local government to find out if that's adequate, and also to have the work inspected to insure it's done properly.

It's referring to the electrical service supplying the house. Most homes in the US are supplied by a single phase service, which is often described as a 120/240 Volt system. If your house is supplied by a three phase system, it could be a 120/208 Volt system.

In both these cases you'll be able to install the equipment you have.

NEMA 14 devices are four wire grounding devices. Which means they'll require two ungrounded "hot" conductors (X,Y), one grounded "neutral" conductor (W), and one grounding conductor (G). When installed on a single phase 120/240 volt circuit, NEMA 14 devices can supply 120 and/or 240 volt loads. A NEMA 14-30 device is designed to supply 30 ampere equipment.

The circuit will require a 30 ampere double pole breaker, and four at least 10 AWG copper conductors. You'll connect one ungrounded "hot" conductor to each of the X and Y terminals. The grounded "neutral" conductor goes to the W terminal. And the grounding conductor connects to the G terminal.