Using events in which one of two neutral B mesons from the decay of an Y(4S) resonance is fully reconstructed, we set limits on the difference between the decay rates of the two neutral B mass eigenstates and on CP, T, and CPT violation in B0B̄0mixing. The reconstructed decays, comprising both CP and flavor eigenstates, are obtained from 88 million Y(4S)→BB̄ decays collected with the BABAR detector at the PEP-II asymmetric-energy B Factory at SLAC. We determine six independent parameters governing oscillations (Δm,ΔΓ/Γ), CPT and CP violation (Re z,Im z), and CP and T violation (Im λCP,|q/p|), where λCPcharacterizes B0and B̄0decays to states of charmonium plus KS0or KL0. The results are sgn(Re λCP)ΔΓ/ Γ=-0.008±0.037(stat.)±0.018(syst.)[-0.084,0.068], |q/p|=1.029±0.013(stat.)±0.011(syst.)[1.001,1.057], (Re λCP|λCP|)Re z=0.014±0.035(stat.) ±0.034(syst.)[-0.072,0.101], Im z=0.038±0.029(stat.)±0.025 (syst.)[-0.028,0.104]. The values inside square brackets indicate the 90% confidence-level intervals. The values of Im λCPand Δm are consistent with previous analyses and are used as cross checks. These measurements are in agreement with standard model expectations.