Question: who is supposed to kill frosch?
Answer: When Natsu says that Frosch won't die, Future Rogue asks Natsu to tell the current "him" to protect Frosch in one year. With one last angry glare, Future Rogue states that if Natsu doesn't do so then Frosch will be killed by Gray Fullbuster. With that, the mayhem ends and Future Rogue returns to his own time.