Eh, I just talk to everyone I see - and when he started sounding suspicious, I shot him. First playthrough. Quite cool when I realized I'd saved the chopper
Yeah, he did sound somewhat strange the first time I played the game, but I gave no thought to it until much later when Everett told me what happened. Then I tried various things with him; killing him immediately, talking to him and killing him, throwing the other mechanic's body on him, talking to him and then to Jock, talking to him, then Everett and then killing him, and so on.

I completed the game 5 times or so all the way through and Paul survived, but now he keeps dieing
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The funny thing there is that one of you must die in the firefight in the hotel; if you survive, he dies, and if he survives, you die. (or at least you become unconscious) This was something I experimented around with quite a bit; the first time I played through, I left the hotel immediately, and so Paul died. Later, I tried a number of different things, including killing all the bad guys in the hotel and on the streets, but he still died, so I concluded that you must die to allow him to live.

(can't see how he would die anyway; he is invulnerable, runs extremely fast and has a ton of ammo

) Although they must be putting you back together or something, since you are still alive later, but heavily damaged.
One a side note, has anyone tried releasing the two greasels in the MJ12 Pacific Rim lab in Hong Kong? Usually they end up doing some wacky things in there with the guards, but the real fun part comes when you release the nearby bum. It is pretty rare, but the bum sometimes is able to run all the way to where the soldiers' breakroom is, with the special agents following him. If this occurs, the normal MJ12 soldiers and the special agents actually start fighting each other. (with the scientists running around in the middle) I have a saved game there; it is really funny to watch that.

The most recent thing I discovered was that one of the police officers in Paris has a reload mod on him, so I just get him angry and kill him to get that. (those mods are rare)