1) "Did Disarming Dumbledore rather than killing him save Draco's life, as Voldemort thought that Snape killing Dumbledore made him the owner and was this part of Dumbledore's plan?"
I suspect you're right: In all likelihood, Voldemort probably didn't consider the fact that disarming would transfer a wand's power. Remember, one of the names of the Elder Wand was "The Death Stick"- as Ollivander said, the wand had left a "bloody trail across history", and thus Voldemort would have expected a more violent transaction to secure the wand's passing.
It's also possible that the Death Eaters didn't mention that Draco disarmed Dumbledore, --but- given that Bellatrix makes a remark on this ("Dumbledore alone, Dumbledore defenseless"), I wouldn't bank on this.--
edit: as pointed out by Janus Bahs Jacquet, no Death Eaters actually saw the disarming, so Voldemort bieng unaware of it taking place is a viable option.
2) "Does Draco realize how close he was to dying when Harry reveals the allegiance of the wand?"
In the film and the book, when Draco spots Harry on platform 9 and 3/4, he gives him a nod of recognition*. Not the friendliest of gestures to someone who actively saved your life several times- remember the fact that Harry flew back to save him from the room of requirement- but still, nice enough considering it was a Malfoy.
3) Is it part of Snape's plan to protect Draco when he promises Narcissa he will do the deed if Draco doesn't?
It is in Snape's interests to protect Draco, certainly: first off, there's the fact that Snape had a history of favouring Draco in potions lessons etc., and Snape was head of his house. Secondly, there's the fact that Bellatrix was present for the formation of the Unbreakable vow between Narcissa and Snape- before which Bella had openly mistrusted and scorned Snape. We know that Snape was, ultimately, a proud man (shouting at Harry towards the end of book 6 "DON'T call me COWARD!"), therefore he would want to accept Bella's challenge to make the vow; not to mention the fact that, as a member of Voldemort's inner circle and influential amongst the other Death Eaters, Bellatrix could pose a huge threat to Snape, should he give her reason to question her identity.
In the unbreakable vow he promised both to aid Draco, but also to protect him- so yes, it was Snape's plan to protect Draco.
As David.S said, my first instict was that Snape and Dumbledore planned to protect Draco's soul, as the act of killing would tear it apart- when Snape asks "but what of my soul, Dumbledore?", it is made clear that the fact that Snape is aware Dumbledore is already dying (and possibly in pain), and the prior agreement they made before, means that he's doing him a service in ending his life.