I have a slightly different take on Elizabeth lying about the Island ... she's safe for now because someone from the other tribe is going. When someone from her tribe is sent, they will understand what she was keeping secret. I think there is a high potential for that to turn into a bond between those two players, and a reason to keep it secret. They can pool whatever knowledge they gain if they choose, or at least be part of a conspiracy of silence. Eventually, of course, it will come out, but I don't think it necessarily has to happen for a while.
I love Rob and Sandra, and I enjoyed this first episode a lot, both their parts in it and the cast. I don't know that I would have thought of negotiating about the fire challenge, but I would certainly have immediately said "what? that's hardly a fair fight, you've been making fire forever and I learned 10 minutes ago!" Maybe that would have led into negotiations, who knows.