Nonlinear Hall responses provide an electrical probe of Berry-curvature dipoles, but they are symmetry forbidden in many pristine two-dimensional metals. We show that layer-selective magnetic proximity provides a symmetry-controlled route to induce and tune anomalous and nonlinear Hall responses in metallic monolayer 1H-NbX₂ (X=S,Se,Te), where the nonmagnetic D₃ₕ crystal has vanishing anomalous Hall conductivity and Berry-curvature dipole. Fully relativistic density-functional theory combined with Wannier interpolation shows that an out-of-plane proximity exchange preserving C₃ generates a sizable sheet anomalous Hall conductivity, σˢʰᵉᵉᵗ_xy∼ 10⁻²(e²/h) in representative active windows, while the Berry-curvature dipole remains zero. Breaking C₃ by introducing an in-plane exchange component, or by using an orthogonal two-sided exchange texture, produces a tunable Berry-curvature dipole and hence a nonlinear Hall response. Its exchange-odd part is linear in the in-plane exchange to leading order in the minimal model; the calculated spectra reach and can exceed |D_y|∼10⁻²mathringA, with the largest and sharpest features in NbTe₂. These trends are rationalized by symmetry analysis and an interface-induced k-linear Rashba-Zeeman minimal model. Within the idealized proximity model, an orthogonal dual-interface geometry further provides component-selective sign reversal of first- and second-harmonic Hall signals in the same Hall-bar configuration.