We present the first results on the Dalitz-plot structure and improved measurements of the time-dependent CP-violation parameters of the process B{sup 0} {yields} K{sub S}{sup 0}K{sub S}{sup 0}K{sub S}{sup 0} obtained using 468 x 10{sup 6} B{bar B} decays collected with the BABAR detector at the PEP-II asymmetric-energy B factory at SLAC. The Dalitz-plot structure is probed by a time-integrated amplitude analysis that does not distinguish between B{sup 0} and {bar B}{sup 0} decays. We measure the total inclusive branching fraction {Beta}(B{sup 0} {yields} K{sub S}{sup 0}K{sub S}{sup 0}K{sub S}{sup 0}) = (6.19 {+-} 0.48 {+-} 0.15 {+-} 0.12) x 10{sup -6}, where the first uncertainty is statistical, the second is systematic, and the third represents the Dalitz-plot signal model dependence. We also observe evidence for the intermediate resonant states f{sub 0}(980), f{sub 0}(1710), and f{sub 2}(2010). Their respective product branching fractions are measured to be (2.70{sub -1.19}{sup +1.25} {+-} 0.36 {+-} 1.17) x 10{sup -6}, (0.50{sub -0.24}{sup +0.46} {+-} 0.04 {+-} 0.10) x 10{sup -6}, and (0.54{sub -0.20}{sup +0.21} {+-} 0.03 {+-} 0.52) x 10{sup -6}. Additionally, we determine the mixing-induced CP-violation parameters to be S = -0.94{sub -0.21}{sup +0.24} {+-} 0.06 and C = -0.17 {+-} 0.18 {+-} …