Question: What happened to the family at the end of the TV series?
Question: What did John said to the spider Smith after he said, "Remember the Proteus," and what did he mean by that?
Answer: He meant (as he says shortly after) that the spiders on the Proteus (that infected Smith) eat their dead/wounded, so when spider Smith's egg-sack is ruptured, the babies eat him.
Answer: Presumably, they're still "Lost In Space." The series ended before a final episode was shot. In the 80's, series creator Irwin Allen considered doing a TV reunion movie with the original cast to bring the Robinson family home, but with the unfortunate passing of Guy Williams, the idea kind of fell to the wayside.