True Peace

Why would Pinchas and the Kohanim, who acted with force, be given the reward of peace? Pirkei Avos holds up the dispute of Shammai and Hillel as an argument for the sake of heaven, and Korach's as the opposite. What exactly is the difference? And why couldn't David HaMelech build the Beis HaMikdash? Peace sounds like keeping an argument quiet, yet the Torah keeps tying it to people who spoke up. Then come three things the Gemara says mean peace when seen in a dream, and a mashal of a father, a torn newspaper and a seven-year-old who finishes far too quickly.