Nope. The current in the ground net is (by definition, Kirchhoffs Current Law) the same as in the power net. Or, a different view but the same result: Every electron that goes into the power supply (at the positive terminal!) has to come out at the negative terminal (ground). Conservation of Mass is a nice law there.
No it's not. Kirchhoff deals with a single loop at a time, not with a whole net.
The decoupling capacitors filter out most of the high frequency content of the current from the power delivery system (i.e. cables to the PCB)
Conservation of mass? Electrons don't have much mass. I guess it even depends on their speed too (although drift speed due to current is low).
The GND plane is also the reference for all signal tracks.
Above a few kHz the main impedance of any track is the loop inductance, and not the DC resistance, and above those frequencies minimizing the loop inductance is the main goal, and that is done by putting a GND track directly below each signal track.
And to avoid getting mad, this is simplified in practice to a full GND plane. A 4 layer PCB (with internal GND layer(s)) has the additional advantage that the GND plane is much closer to the tracks. It goes from approx 1.5mm (the PCB thickness) to 0.1mm or so. so a factor of 10 reduction in the loop inductance.
As long as the local decoupling (and buffer caps) is good enough to keep the frequency content of power delivered to the PCB well below a kHz, then the main concern for the power net is the DC resistance. All the higher AC currents exist then only between the decoupling caps and the IC's (and this distance must be minimized).
I've also done a simple search. The man with the grey beard appears to have a name. (It's Rick Hartley).
The youtube video I mentioned earlier is:
[LIVE] How to Achieve Proper Grounding - Rick Hartley - Expert Live Training (US)