  We present a series of measurements based on K -> pi+pi- and K -> pi0pi0
decays collected in 1996-1997 by the KTeV experiment (E832) at Fermilab. We
compare these four K -> pipi decay rates to measure the direct CP violation
parameter Re(e'/e) = (20.7 +- 2.8) x 10^-4. We also test CPT symmetry by
measuring the relative phase between the CP violating and CP conserving decay
amplitudes for K->pi+pi- (phi+-) and for K -> pi0pi0 (phi00). We find the
difference between the relative phases to be Delta-phi = phi00 - phi+- = (+0.39
+- 0.50) degrees and the deviation of phi+- from the superweak phase to be
phi+- - phi_SW =(+0.61 +- 1.19) degrees; both results are consistent with CPT
symmetry. In addition, we present new measurements of the KL-KS mass difference
and KS lifetime: Delta-m = (5261 +- 15) x 10^6 hbar/s and tauS = (89.65 +-
0.07) x 10^-12 s.
