Your question about protection is a very important one. Every electrician, technician working with heavy machinery, and electrical engineer should know how these things work.
All About Circuits published a very comprehensive online compendium about electronics and electrical engineering. For your question, I recommend reading this article about safety in circuit design.
In short, current chooses the shortest path to a lower potential. Without a grounded metal case, your body may become a path to a lower potential (earth). Your body may not be the best conductor, having e.g. 1000 Ohms, but it's still many orders of magnitude less than air.
Your kitchen floor is approximately earth potential. Buildings, soil, etc are not very good conductors, but they still have a low resistance compared to, say, air.
Earth's soil may have a resistance of a few Ohms, maybe tens of Ohms, it depends on many factors. What's certain is that it does conduct.
Current choses the shortest paths. What's more, a large contact surface will create more paths for the current to flow, thus lowering the resistance of something which at first glance is not a good conductor.
To measure single-phase power, simply measuring voltage and current does not yield actual power with any precision. Any power factor issues will skew the results, often badly.
Consider instead a solution like this one from SiLabs with their Si8902, which uses digital-side isolation, not line-side. Or here is another approach from Linear Tech using their LM2940, where isolation is at line side. Similar isolated solutions exist from Texas Instruments, and many other companies.
If you must measure in discrete parts,
- Measuring current on both live and neutral legs is often useful - a difference would indicate an earth leak inside the domestic network. Inductive clamps are safe enough.
- Measure voltage across live to neutral using either an isolated voltmeter or an isolating voltage sense IC
- Measure phase on both voltage and current sense channels, so you can have a PFC correct power figure such as the utility company bills you for.
An important point to keep in mind:
Most utility companies frown upon any equipment connected on the distribution side of your domestic entry point / fuse box - all devices including power monitoring must be on your side of the fence. Also, connecting anything at all beyond the fuse box may violate UL or equivalent certification for your geography, leaving your home exposed to diminished insurance coverage.
Best Answer
There is such thing as single wire power distribution systems that use the ground (earth) as the return. They are often used in big rural places where the costs of wire are high like Australia...
https://en.wikipedia.org/wiki/Single-wire_earth_return
But even in these systems typically there are two (or more) wires coming into the house. This is because the long distribution wire is run at very high voltages to keep the current low. These voltages would be unsafe and unuseful to bring into a home, so they are stepped down with a transformer to a usable voltage and sent into the home over a normal two (or more) wire connection.
More locally, you could connect one side of a light bulb to the hot wire in your house and the other side to a rod driven into the earth and, depending on the soil condition (moist and dense is better) and how close the nearest other earth connection is, it is possible that light would turn on. This is not so good for a few reasons though, among them...