We report on mass and lifetime measurements of several ground state charmed and bottom baryons, using a data sample corresponding to 9.6 fb(-1) from p (p) over bar collisions at pffisffiffi root s = 1.96 TeV and recorded with the Collider Detector at Fermilab. Baryon candidates are reconstructed from data collected with an online event selection designed for the collection of long-lifetime heavy-flavor decay products and a second event selection designed to collect J/psi -> mu(+)mu(-) candidates. First evidence for the process Omega(-)(b) -> Omega(0)(c)pi(-) is presented with a significance of 3.3 sigma. We measure the following baryon masses: M(Xi(0)(c)) = 2470.85 +/- 0.24(stat) +/- 0.55(syst) MeV/c(2); M(Xi(+)(c)) = 2468.00 +/- 0.18(stat) +/- 0.51(syst) MeV/c(2); M(Lambda(b)) = 5620.15 +/- 0.31(stat) +/- 0.47(syst) MeV/c(2); M(Xi(-)(b)) = 5793.4 +/- 1.8(stat) +/- 0.7(syst) MeV/c(2); M(Xi(0)(b)) = 5788.7 +/- 4.3(stat) +/- 1.4(syst) MeV/c(2); and M(Omega(-)(b)) = 6047.5 +/- 3.8(stat) +/- 0.6(syst) MeV/c(2): The isospin splitting of the Xi(-0)(b) states is found to be M(Xi(-)(b)) - M(Xi(0)(b)) = 4.7 +/- 4.7(stat) +/- 0.7(syst)MeV/c(2). The isospin splitting of the Xi(0,vertical bar)(c) states is found to be M(Xi(0)(c)) - M(Xi(0)(c)) = 2.85 +/- 0.30(stat) +/- 0.04(syst) MeV/c(2). The following lifetime measurements are made: tau(Lambda(b)) = 1.565 +/- 0.035(stat) +/- 0.020(syst) ps; tau(Xi(-)(b)) = 1.32 +/- 0.14(stat) +/- 0.02(syst) ps; tau(Omega(-)(b)) = 1.66(-0.40)(+0.53)(stat) +/- 0.02(syst) ps: