How do I verify that the ground wire in my home is grounded?

Your approach is basically correct. (In the exclusion of zero line and ground line confusion) your home circuit grounding is basically normal.

1, multimeter single ground line, the other suspended, in the 200V file reads 2.7V state indicates that the line has an induced voltage, and often this induced voltage comes from the line of high harmonics. Commonly known as clutter, from the surge voltage, switching power supply, near the radio and television stations, hairdryer; in the case of high harmonics exist in the wire, through the diode of the meter (such as the meter head protection diode) detector, you can detect the voltage in the case of a single line;

2, connected to the zero line, the degree of 1.2V -- the same reasoning with the 1, the detected readings are random, both 1.2 or 2.7; you change the point measurement value will change.

In the early days of computer engineering, ct nuclear magnetic medical devices were very concerned about line harmonics. The solution was not a matter of good or bad grounding, it was the need for EMC of the equipment and the addition of filtering equipment. At home it doesn't matter