2 pins would be plenty. 12v Power, Ground, and an overlaid capacitively coupled 2 way data comms running at a few hundred khz to send and receive status messages, fan speeds, model/serial numbers, firmware/ temperatures, on/off commands, etc.
This is actually the best bit, incredibly smart idea. It's a kelvin connection to ensure that you get 12V at the motherboard, regardless of power dissipation in the wire.
No, modern desktop can easily use up to 30A constant load. No way to provide so much over 1mm wires at 12V
Each individual terminal, formally called a Molex mini-fit junior terminal, is rated either 7.0A (typical for those with 2 contact springs) or 9.0A or 13.0A (for those with 4 contact springs.)
As you can imagine, most cheap PSUs and wire harnesses are made of terminals with 2 contact springs, so the three 12V wires on the ATX12VO spec allow a max of 3×7.0A = 21.0A or 252 watts.
As to voltage drop caused by resistance in the wire, it will be sufficiently small with 16AWG wire which will easily carry 7A over the short distances in a PC case.
(I thought DC current used the volume of the wire and AC the surface area, so I'm a bit surprised that wire ratings don't distinguish AC and DC. Though I suppose heat dissipation is determined by the surface area so perhaps that makes sense.)
I used an calculator and got 8416.7115um for 60hz. Which is 8.4mm. So not an issue for power wiring under 0000.
Apply this simple rule of thumb: watts become heat. The only major exception to this is where the power has exited the computer via USB or similar.
Still a single pin is probably something like a #18 gauge and would only be good for 10A before it gets too warm for comfort.
That hasn't been true for a long time. Nearly every motherboard for many years has a separate "ATX12V" plug dedicated exclusively to the CPU voltage regulator input. According to Wikipedia (https://en.wikipedia.org/wiki/ATX12V), the first CPU which needed it was the Pentium 4 from the early 2000s.
As for the GPU, the PCI Express slot can only go up to 66W in the 12V rail (https://en.wikipedia.org/wiki/PCI_Express#Power), and that's a software-enabled special case for GPUs (the normal limit being 25W for long slots and 6W for the short x1 slots), so higher-power GPUs need one or even two separate power plugs.
No. You are gonna burn wires.
I suspect the real reason to use many smaller wires instead of two big ones is cable flexibility. There is no electronic problem with two big ones, unless you repeatedly shoot yourself in the foot. Don't do that.