So, a little tidbit of fluff I have often had trouble with. Many times, sources say only a few individuals are allowed into the throne room, to see the Emperor. Now, certainly this makes sense, from a security standpoint, and he isn't going to say or do much, so there is very little point to seeing him, but I was led to believe that Soul-bound psykers had to be taken before him. Even if there are trillions of Humans in the galaxy, and only a small percentage of them are soul-bound, that still adds up to a lot of people who have seen him, not including the various magos who preserve the Golden Throne (as best as they can today), and the Companions (His Custodes bodyguards). So, what's the deal? Is there an antechamber, and that's all the further most go? Are they just going by a percentage? What's up?

Dumb extra, why is he decayed? One would think that, if they could insert Roboute Gullimen, the Ultramarines Primarch, in a stasis field (and even make a bit of a tourist attraction out of him (millions of pilgrims come each year to catch a glimpse of the only remaining loyalist Primarch, even though it is an Astartes-controlled planet), why couldn't the Emperor's body be preserved thus, so that he might, someday, return to it?

I could be wrong, but I was under the imperssion that soul-binding was done in one of several chambers within the Golden Throne, and not necessarily in the presence of the Emperor himself.

And I think that full stasis would prevent the Emperor from being able to broadcast the Astronomicon- he has to be carefully held midway between life and death to remain psychically active. That's my guess.

About Astropaths, all it says is the procedure takes place before the Golden Throne, and the Golden Throne is the size of Himalayas, so it's relatively conceivable to see the Throne without seeing the Emprah in the process.

About the decay thing, the guy was never put in stasis, because his psychic power was needed to light up the Astronomican, and to keep the webway gate beneath the Golden Throne shut, lest daemons overtake Terra.

SOUL BINDING

The Soul Binding is a ritual conducted by the Adeptus Astra Telepathica of the Imperium of Man which is responsible for creating Astropaths. Normal psykers are unable to transmit telepathic messages across vast distances through the warp with this being only accomplished by the special talents of Astropaths. These individuals undergo special training over many years before taking part in this special rite where their minds are brought before the great psychic might of the Emperor himself. During this process, a portion of the Emperor's vast essence is transfered into that of the Astropath. The transference process is a traumatic experience with not all being successful despite many years of training with some not surviving and those that do lose much of their sanity. The most visible result of the Soul Binding is damage to the sensitive nerves of the eyes which almost all Astropath's blind leaving behind distorted, sunken empty eye sockets. However, the ritual imparts them greater psychic skills which tends to make up for their lost eyesight and they tend to not act as if are blind.

Astropath training ultimately ends with this rite which is a techno arcane initiation ritual that greatly opens their minds to the warp. The ritualistic soul binding to the Emperor can protect many psykers from the perils of the Warp. The entities of the warp are a hideous threat to those psykers who have not undergone the Soul Binding ritual. According to legend by M41, the first psyker to take part in the Soul Binding ritual was Malcador the Sigilite who became forever linked to the Master of Mankind.

THE GOLDEN THRONE

Originally built to provide access to the Eldar Webway, the Golden Throne took the form of a bulky machine-like chair suspended over gigantic mechanised doors made of gold metal. The doors were said to be large enough for a Warhound Scout Titan to walk through unbowed. The chair was linked to the portal by huge bundles of cables, wires and conduits. The whole machine was made of the same golden metal. The throne was built at one end of a vast hall big enough to house up to six fully equipped Space Marine Companies. This was the Emperor's main laboratory, which was itself at the centre of his underground complex, known as the Imperial Dungeon. Even after the Throne's construction, the lab remained littered with other huge machines and storage crates. Hundreds of red-robed technicians and labourers worked in the lab.

The Emperor built the throne as a means of entering the Webway. Having this fixed point of entry was meant to free humanity from its reliance on Warp-ships and astrotelepathy, since humans could simply enter the Webway and emerge wherever they chose in the galaxy. He sent armies of workers through the portal and had them construct a new short section of Webway linking to the rest of the abandoned Eldar network. Since the original Webway was built of a psychically resistant material which the humans could not replicate, the Emperor used his powers, via the Golden Throne, to protect the human-built section from the Warp.

The Golden Throne is connected to a massive Warp beacon known as the Astronomican which generates a system of signals making faster-than-light travel in the Imperium possible

.In the last year of M41, Techpriests discovered failures in the mechanisms of the Golden Throne that are far beyond their ability to repair.

IMPERIAL PALACE - INNER PALACE

The Inner Palace, the Sanctum Imperialis, is the massive throne room at the heart of the Palace, where the arcane machinery comprising the Golden Throne keep the Emperor's few living cells alive, providing an anchor point in the warp for his mighty spirit. Tech-priests of the Adeptus Mechanicus constantly maintain the vast Golden Throne. In an arena before the Emperor himself, psykers are soul-bound for Imperial service as Astropaths. Standing before the Inner Palace is the massive Eternity Gate, forged of the strongest materials. Two Titans stand guard over the Gate in its damasked beauty and immeasurable strength.

ADEPTUS CUSTODUS

The Adeptus Custodes are the guardians of the Imperial Palace and the Golden Throne, as well as being the personal bodyguard to the Emperor. A small elite of three hundred Custodes, known as the Companions, form the Emperor's personal bodyguard and never leave his side. Due to the vast size of the Imperial Palace, the Custodes always act as a defensive army1. In M41 the Custodes themselves never leave Terra, and only rarely leave the Palace.
It is the Adeptus Custodes that decide who may enter the throne room of the Emperor, and when.

The above was taken form the Lexicanum website.

I hope this large amount of fluff gives you the answers you need.

There are a variety of artworks showing the Emperor on the Golden Throne: examples are here , here and here.

Just as a bit of a fun aside, I had always taken the view that the differences in the "official" images of the Emperor and the throne can be explained by an elaborate body double scheme operated by the Adeptus Custodes. I imagine that the Imperial Palace contains quite a few "fake" Emperors attached to life support machines, intended to be used as body doubles to foil assasination attempts that actually make it within the palace.