The (nu) over bar (e) - e elastic scattering cross-section was measured with a CsI(Tl) scintillating crystal detector array with a total mass of 187 kg at the Kuo-Sheng Nuclear Power Station. The detectors were exposed to a reactor (nu) over bar (e) flux of 6.4 x 10(12) cm(-2)s(-1) originated from a core with 2.9 GW thermal power. Using 29882/7369 kg-days of Reactor ON/OFF data, the Standard Model (SM) of electroweak interaction was probed at the 4-momentum transfer range of Q(2) similar to 3 x 10(-6) GeV2. A cross-section ratio of R-expt = [1.08 + 0.21 (stat) + 0.16 (sys)] x R-SM was measured. Constraints on the electroweak parameters (g(V), g(A)) were placed, corresponding to a weak mixing angle measurement of sin(2)theta(W) = 0.251 +/- 0.031 (stat) +/- 0.024 (sys). Destructive interference in the SM (nu) over bar (e)-e processes was verified. Bounds on neutrino anomalous electromagnetic properties (neutrino magnetic moment and neutrino charge radius), as well as non-standard neutrino interactions were placed. We summarize the experimental details and results, and discuss projected sensitivities with realistic and feasible hardware upgrades.