Explaining consciousness is difficult. We still don't certainly know how and why we are conscious. For me, thinking is using previous input and memories to find connections and patterns, and depending on what I want to do, creating a similar thing or a different one. "Different" can be similar to past knowledge.
As for how we process input to begin with, we can explain it by referring to parts of the brain, but how *does* that happen anyway? It's easy to say "neural pathways", but our ability to learn and retain is still interesting, but not wholly mysterious, to me. The reason I say not wholly is because a lot of it is rooted in survival, which is explainable in detail and makes sense (think conditioning).
1) That is true. My mother tells me that we are from God's light and we return to it. I think it's a nice idea. Here, "we don't stop existing" comes in terms of heaven. 2) Without meeting them, one cannot be sure. Those people exist as mere hypotheticals to me. I can come up with a person and their life and chances are they exist. For them to exist to me, I simply have to strongly believe in it.