You ask too many questions!
There are hundreds of capacitors in a receiver with very diverse functions.
I think however you are referring to power supply caps, properly known as smoothing capacitors.
First you have to convert the AC line input to the various AC voltages required in the device. This is done with multiple secondary transformer taps.
Now lets just take a single voltage. The first step is full wave rectification.
Half wave rectification is not very useful
Here we have an AC line voltage and one rectifier. If you look at the scope you see only the positive parts of the wave have been rectified and there is a gap between the positive deflections on the scope.
There are basically two common ways of using both halves of the AC input.
The bridge rectifier.
The other is the center tapper balanced almost always used with tube circuits.
Now you will see in both these examples on the scope you see all positive deflections, but the are positive waves one after the other.
Now we want an elevated straight line, like you would get from a battery.
So a smoothing capacitor is added, like this.
A capacitor will store a charge, and so it smooths the undulations.
Now the capacitor has to have enough capacity to supply the load between the the dips and peaks of the undulating waveform. If it is inadequate, then power ripple will occur, which is highly undesirable.
Now if the capacitor is of a value larger than required for smoothing, then the capacitor can make excess current available to the load for very brief periods. This is most useful for providing current to an output stage, to supply the current to provide the apparent power required for loads with negative phase angles. Since this power is given back this is an ideal application for using capacitors of higher value than required to meet true power requirements. However capacitors will not increase the true RMS power of an amp in a meaningful way.
In modern circuits, power supplies are highly regulated. There are thousands of topologies for regulated power supplies.
Here is and example.
If you understand this, I think you will see that any claim for an AC cable or receptacle to improve the sound of an amp is totally bogus.
Also power conditioners are largely bogus.
Regulated power supplies will keep the DC supply voltages in tight limits for brief periods, and for excess voltage within specified limits indefinitely. However they can only handle voltage sags very briefly.
Voltage sags are also highly deleterious to modern microprocessor electronics.
To handle sage requires a battery.
That is why I keep telling you guys, that proper protection requires good surge protection, preferably whole house, and a UPS which has a battery to control sags.