We present first measurements of the phi-meson elliptic flow (v(2)(p(T))) and high-statistics p(T) distributions for different centralities from root s(NN) = 200 GeV Au+Au collisions at RHIC. In minimum bias collisions the v(2) of the phi meson is consistent with the trend observed for mesons. The ratio of the yields of the Omega to those of the phi as a function of transverse momentum is consistent with a model based on the recombination of thermal s quarks up to p(T)similar to 4 GeV/c, but disagrees at higher momenta. The nuclear modification factor (R-CP) of phi follows the trend observed in the K-S(0) mesons rather than in Lambda baryons, supporting baryon-meson scaling. These data are consistent with phi mesons in central Au+Au collisions being created via coalescence of thermalized s quarks and the formation of a hot and dense matter with partonic collectivity at RHIC.