Using a proton-proton collision data sample corresponding to an integrated luminosity of 3 fb(-1) collected by LHCb at center-of-mass energies of 7 and 8 TeV, about 3800 Xi(0)(b) -> Xi(+)(c)pi(-), Xi(+)(c) -> pK(-)pi(+) signal decays are reconstructed. From this sample, the first measurement of the Xi(0)(b) baryon lifetime is made, relative to that of the Lambda(0)(b) baryon. The mass differences M(Xi(0)(b)) - M(Lambda(0)(b)) and M(Xi(+)(c)) - M(Lambda(+)(c)) are also measured with precision more than 4 times better than the current world averages. The resulting values are tau(Xi b0)/tau(Lambda b0) = 1.006 +/- 0.018 +/- 0.010, M(Xi(0)(b)) - M(Lambda(0)(b)) = 172.44 +/- 0.39 +/- 0.17 MeV/c(2), M(Xi(+)(c)) - M(Lambda(+)(c)) = 181.51 +/- 0.14 +/- 0.10 MeV/c(2), where the first uncertainty is statistical and the second is systematic. The relative rate of Xi(0)(b) to Lambda(0)(b) baryon production is measured to be f(Xi b0) B(Xi(0)(b) -> Xi(+)(c)pi(-)) B(Xi(+)(c) -> pK(-)pi(+))/f(Lambda b0) B(Lambda(0)(b) -> Lambda(+)(c)pi(-)) B(Lambda(+)(c) -> pK(-)pi(+)) = (1.88 +/- 0.04 +/- 0.03) x 10(-2), where the first factor is the ratio of fragmentation fractions, b -> Xi(0)(b) relative to b -> Lambda(0)(b). Relative production rates as functions of transverse momentum and pseudorapidity are also presented.