1) Peter compares the purging judgment that will befall the earth at the second coming with that of the flood, saying "the world that then existed perished, being flooded with water." Now, someone reading that in the manner of a post-Enlightenment literalist would reply, "C'mon Peter, we all know that the earth didn't perish at the flood, it was just purged. We still live on the same earth!" But such a person would be missing Peter's point. Seeing that he compares the fiery judgment of the end of the age with the flood of old, it would be just as wrong of us to suppose that the destruction which Peter envisions will be comprehensive. Rather, just like the flood, it makes the most sense that it would be a purging, renovating judgment, and not a complete annihilation.
2) The word translated "melt" in v. 10 and "dissolved" in v. 11 and 12 literally means "to loose" or "be undone", and (if we trust the NU) the word rendered "burned up" in v. 10 by the NKJV and other translations (κατακαίω) is actually a mistake and should be the word τραχηλίζω, which would be translated "laid bare" or lit. "found". Again, this accords nicely with the picture Paul paints in 1 Corinthians 3:11-14, where only the works that are not done unto God (metaphorically called "wood, hay, straw") are destroyed in that day, and all those that are performed on the foundation of Christ ("gold, silver, precious stones") last into the age to come. Like I said, the fire is a fire of testing, a refiners fire (cf. Mal 3:2-3).