: 1) When the ring falls into the Cracks of Doom with Gollum, this is the downfall of Sauron, second and last. Does the destruction of the ring kill Sauron, as I think I have heard someone said(or at least how I interrpreted what was said)? But if this is so how could he not know that the ring was still in tact?

No, Sauron was not killed by the destruction of the One Ring. He was a maiar spirit, and for all intents and purposes, unless Eru or the Valar unmade him (and I don't even know if that is possible) then Sauron could not die.

: 2) Sauron was master of the one ring. And the one could control all of the others. Sothis means that Sauron could control the nine even when the ring was not in his possesion (what I have peiced together) But had the ring actually been destroyed, would he still be able to control the wraiths? And wouldn't this tell him his ring was whole long before he caught gollum?

Well, Sauron could not control the Three. There is no mention of whether any lesser Rings were under the One's control either. However, to your question, I think there is some confusion that we need to handle. Sauron tainted the Nine and the wearers of the Nine were changed into wraiths (i.e. the Nazgul). Sauron was a necromancer and thus he had power over the dead, such as wraiths. Once Sauron held their Rings, he didn't need the One to control them, as is evidenced by the fact that the Nine were in his control and yet he didn't have the One.

The One was more greatly a recepticle for a vast amount of Sauron's personal power, thus when it was destroyed he himself fell greatly, to the point that he could never rise again.

It wasn't a matter of whether Sauron could control the Nine if the One was destroyed. Once the One was destroyed Sauron had no more power whatsoever (or so little that it didn't matter), and neither did any of the other Rings. All the Rings were bound up with the fate of the One, this is why the Three faded, why Frodo's coming to Loth Lorien was the "footsteps of doom" to all the elves had created. Whether Sauron knew the Ring was extant or not is a point for some debate. Though it seems even prior to Gollum's capture he knew that it did, as he had the Nazgul and his agents searchign for it, and offering rewards for its return. Thus the question of whether Sauron could control the Nine if the One was destroyed is rendered moot, by the fact that Sauron himself could control nothing once the One was destroyed.

-RR