The database don't mention that Snake killed him in Metal Gear 2.
Your second question has been nagging at me since I finished the game. Trying to piece together Ocelot's intentions in MGS and MGS2 almost seems impossible. Even before Metal Gear, he was already working against the Patriots with Big Boss, until Snake defeated him. After that he was working with Eva to retrieve Big Boss's body. If Liquid and Solidus both wanted to create an "Outer Heaven" like Big Boss and Solidus even wanted to take down the Patriots as well, why did Ocelot use them and throw them away?
As for your third one, I think someone in this thread explained it quite clearly:
If Ocelot had to hide from the Patriot AI, he'd need three things.
False DNA
False Biometric signature
False brain wave pattern. These are the three things that make up an ID to the AI system.
Simply not having nanos would not allow him to access SOP. He needs nanos, but they cannot be attached to his own body. He would access nanos through a proxy(his robotic arm), while the nanos were stored within an organic extension(Liquid's hand).
time to explain:
Now, Ocelot could have simply ridded himself of Nanomachines, but that would have raised suspicion in the AI and also had disconnected him from SOP. That doesn't help him. He must have a way to connect to the AI.
But..he could still use nanomachines if he quarantined them to Liquid Snake's arm. This was done by creating a device to sustain his arm while masking his own DNA. A proxy. A proxy is used by a computer accessing a server, through another server, to keep it anonymous. The robotic arm was the proxy. It kept Liquid's hand alive through technology, but prevented the mingling of Ocelot's DNA or Nanomachines with that of Liquid Snake's, which were quarantined within his hand. Essentially, his hand was registered as a living person, while Ocelot himself remained anonymous.
So Liquid Snake's arm contained his nanomachines, DNA, Biometric Signature, and through wiring, it used Ocelot's brain waves to keep it alive, give it movement, and also complete the SOP ID that Ocelot now used. The psychotherapy reshaped his brainwaves to match the data recorded in Liquid's nanomachines, turning him into Liquid Snake's memetic doppleganger. This also allows Ocelot to NOT contain 4th gen Nanomachines in his own body, protecting him from the effects of the SOP withdrawl and removing him from having to register himself using 4th gen nanomachines. This hid him away.
So when this person(Liquid Ocelot) registered with the Patriot AI, it wasn't a person they are monitoring. It was not a threat. It was most likely not identified as Liquid died before the system was put in order. The interesting thing is that this turned Liquid Snake's right arm into a controller for SOP once he took the system. When he aimed and fired with that magic arm, he literally sent administrative commands through his arm and into SOP, ordering his soldiers to fire. His brain made the command and the system recognized the signature expressed through Liquid's hand and it was sent through his arm into the system, and delivered to the soldiers through GW.
That arm itself was a proxy server between himself, GW, SOP, and the soldiers now connected to it.
