I haven't read the entire thread in detail. It's now too long and filled with fluff it's completely unreasonable to expect anyone to read thoroughly.
Briefly: yes it's possible to measure the mains with a standard x10 probe, if the neutral is connected to mains earth. Just connect the probe to the phase conductor and it will work. Obviously don't connect the neutral of the grid to earth, as the only the distributor is allowed to do that. In the case of an inverter: check the resistance with a multimeter, when it's connected up, but switched off. It's generally a good idea to earth the neutral of an inverter to prevent it from floating at high voltages. Read the manual. If in doubt, use two x10 probes: one on the live and the other on the neutral and the math/differential function.
As mentioned above, a small mains transformer is also a decent option. It won't introduce any noticeable distortion on a pure sine wave, but perhaps a little on the modified sine wave. A toroidal transformer is better. I've found small mains transformers are generally good up to 10kHz, but obviously the losses will be higher with increasing frequency. I'm purely referring to using one for voltage measurement, but to power anything.