The MagSafe power adapter, like nearly all power adapters for modern electronic equipment, is a switching (switched-mode) power supply.
Switching power supplies achieve their light weight and small size by using smaller, lighter transformers for voltage conversion, which require high-frequency AC input to operate. This high-frequency input is produced by a separate circuit which rapidly switches the low-frequency input on and off (hence “switching”), and in fact does so controlled by feedback from the DC output side in order to achieve a tightly-regulated DC output. This regulation itself is also something that varies over time as the input and the output load change.
So, there's lots of varying electrical currents, and therefore varying electric and magnetic fields, inside a switching power supply. These fields exert mechanical forces on the components within the power supply, which may cause them to vibrate and therefore produce sound!
In a well-designed power supply, the basic frequencies are chosen to be above the range of human hearing (and the components most subject to vibration may be held down especially firmly). However, for various reasons (waves hands, I don't actually know the details) you may get effects at fractions of those frequencies which you can actually hear.
In your particular case, if the power supply is running overloaded (or at the upper limit of its capability), then that might put some subsystem oscillating at the upper end of audibility, producing the sort of noise you're hearing.
You can often hear noise from cheap power supplies (e.g. USB chargers) when they are unloaded (nothing connected to the output), and hear it shift out of audible range when you connect something.
(Disclaimer: I Am Not An Electrical Engineer; this is just bits and pieces I've picked up. These folks would have the whole story; e.g. this answer which is a bit short on detail. But, I hope I've at least somewhat demystified why apparently solid lumps of electronics can make noise. (If anyone sees a factual error or can explain better, please feel free to edit this answer!))
Depending on how old the charger is, it is possible the agent causing the discoloration is leaching through from what the casing covers instead of being caused by an external source. In this case, bleaching and cleaning will affect only the surface of the cable.
I used to have several cables like this, on old barrel-shaped (non-MagSafe) chargers, but when the laptops were recycled, so were the chargers, so I don't have anything to dissect to prove my assertion.
The power charger can also get quite hot when charging, and if the charging cable is partially or wholly wound on the charger body's cable-storage fingers, they may become very hot as well, causing some of the discoloration you see. I always fully unwind the connection cable before charging.
Best Answer
Magsafe cables only carry voltages ranging from 14.5 to 20 volts, which is not nearly enough to be able to feel. For more information, see this Electrical Engineering Stack Exchange question. You would not be able to touch the actual conductors anyways as the metal "wire" that is visible in this picture does not carry any current, as it is just shielding around smaller insulated wires. It is unlikely for arcing to occur, but you should still get the charger replaced soon. Like iPhone and iPad chargers, always buy MagSafe chargers from an Apple Store or the Apple website as ones bought on eBay and Amazon are known to be non-UL listed counterfeits.