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In topological Dirac and Weyl semimetals, nontrivial conical bands with Fermi-arc surfaces states give rise to negative longitudinal magnetoresistance due to chiral anomaly effect and unusual thickness dependent quantum oscillation from Weyl-orbit effect, which were demonstrated recently in ferromagnetic Weyl metal SrRuO₃ (SRO) thin films. In this work, we report the experimental observations of large nonlinear and nonreciprocal transport effects for both longitudinal and transverse channels in an untwinned Weyl metal of SRO thin film grown on a SrTiO₃ substrate. From rigorous measurements with bias current applied along various directions with respect to the crystalline principal axes, the magnitude of nonlinear Hall signals from the transverse channel exhibits a simple sinα dependence at low temperatures, where α is the angle between bias current direction and orthorhombic [001]_o, reaching a maximum when current is along orthorhombic [1-10]_o. On the contrary, the magnitude of nonlinear and nonreciprocal signals in the longitudinal channel attains a maximum for bias current along [001]_o, and it vanishes for bias current along [1-10]_o. The observed α-dependent nonlinear and nonreciprocal signals in longitudinal and transverse channels reveal a magnetic Weyl phase with an effective Berry curvature dipole along [1-10]_o, accompanied by 1D chiral edge modes along [001]_o.