1. No, it won't work. House mains are sine wave, alternating current which is changing direction 50 times per second (EU) or 60 times per second (US). Even if possible, changing frequency will cause many of household appliances to malfunction, not to mention burnt transformers and motors which are designed to work with sine wave only and at specific frequency. You can use Spooky2 to generate 10Hz and transmit through custom made coils/antennas but not by plugging directly into mains. Besides, connecting Spooky2 OUT to the ground node will direct or short it's signal into the ground, not the "live" wiring.
2. You can do it if you want.
Because the output has got a short circuit protection unit that limit the maximal amount of current.
But what is the effect?
The inducing of current into the earth connection ("in the range of" +-132 mA) has no effect on the LINE voltage therefore this will not "changing the electrical frequency, in the entire house".
The Answer to "not sure of waveform" is : Sinus waveform.
(The line voltage exists between the N and the L connection of the power connection plug.
The PE (Earth) connection is a protection line that should blow the fuse if a electric isolation fault will happen. It contains in its normal operation state no current and should have a low input resistance near Zero Ohm.
But there is a voltage of : 0.3 Ohm x 132 mA = 39.6 mV over the PE connection. It is not Zero.
Maybe this could be a way to transmit a frequency over the whole electrical connection of the building ?
One Output pin on a PE over the electric system and one connection of other pin to a direct earth connection.)
3. Regarding square waves:
Brain will more likely lock-on (entrain) when sine waves are used, not square pulses. Sine waves which are natural produce rotating magnetic field with smooth gradual transitions between build up, collapse and reversal. Personally, I would not leave such generator running all night as it may inhibit dreaming and proper rest. Brain is very sensitive and power levels for such transmission don't have to exceed couple mW.
For more details, please check the link: