Let me start by pointing out the minimum nominal voltage of household electrical power system is 110 vac, not 10 vac. 10 vac, 60 Hz is considered low voltage with respect to electric shock risk.
Say a person touch the live wire as shown in the picture, the current
will flow through him and dissipates into the ground in "rings" as
shown in the picture right?
Current will flow through the person and back to the grounded connection of the voltage source through the soil.
(since the system is grounded at the source so the voltages are not
"floating" as in an isolation transformer) the fault current through a
person does not really “return” to the source as drawn in pencil
That is not correct. Current will actually flow through the person and return to the source through the soil, as shown, but possibly through various paths.
at least not all of it anyway (in the sense that all the current that
went through the person actually traveling back to the source since
the current dissipates into the ground in rings),
The term "dissipate" in your picture simply refers to the fact that there are multiple potential parallel paths in the soil for current to flow as it spreads out. However all of the current returns to the source. It should be noted, however, that power distribution systems are connected to earth ground at multiple locations. Therefore, the current flowing through the body may be split up and return to multiple ground connection points.
Just how exactly does the current return to the source? assuming that
the resistance of a person is 10 ohms.
As already pointed out, the current returns to the source through the earths soil. How much current flows through the body depends on multiple factors.
One factor is the body's electrical impedance, which varies with voltage. At 10 vac60 Hz the total body impedance from hand to foot, under dry contact conditions, is over 5000 ohms with most of the impedance in the skin. The minimum internal impedance of the body (impedance minus the skin) is over 500 ohms. So for all practical purposes in your example the current through the body to ground would be less than 2 mA, assuming zero impedance in the ground path. Another factors is whether or not the person's foot wear is acting as insulation. Also the impedance of the can vary depending on local soil conditions.
The thing that really confuses me is how would current return to the
source, but as you said as long as there's a voltage potential all the
current WILL return to the source right? I was confused about since
current spreads out pretty much uniformly after it enters the ground
why would all of it return to the source since the earth is so big and
the voltage potential at say 50m away from the person's feet is
already 0 –
You know, of course, that there does not need to be voltage difference for current to flow in a conductor. Similarly, there does not have to be a potential difference between the persons foot and the grounding rod for current to flow.
If one were run a copper wire connected to your persons foot under the ground and connect the conductor to the grounding rod that connects the power source to ground, both the persons foot and the ground rod will be at the same potential. We call it zero simply because that is what we assign the potential to be in the earth. Yet current will readily flow through the person and return to the power source through the copper conductor. The reason, of course, is the potential difference is between the persons hand and ground, the latter of which is theoretically at the same potential as the grounding rod (but really isn't because there is always some impedance in the earth path). The soil is simply a replacement for our copper wire (though it is never as good as the copper wire).
Hope this helps.