Can electric bulbs be powered by connecting the negative terminal to earth?
Yes and no.

Yes, because the earth cable is connected to the neutral at some point. In some country this is done at the entry point of every buildings, in other it's earlier. Thus the circuit will be closed and the bulb will light up.

No, because in nowadays house, residual current circuit-breakers are used. If the return current is flowing through the earth cable and not through the neutral cable (>20mA typically) the breaker will break and your bulb won't work.

About your tester:
The human body that touches a terminal of the light included into your tester acts as a capacitor. This is called "Body capacitance". Because the other terminal is connected to an AC source (the main), a current (very very small) flows through the tester and it lights up.