Altermagnets enable spin-split bands and anomalous transport phenomena with vanishing net magnetization, yet the symmetry-governed dependence of their optical and spin transport responses on the Néel-vector orientation remains largely unexplored. Using first-principles calculations and systematic magnetic point group analysis, we establish the complete response tensor forms dictated by the magnetic point group for typical altermagnet CrSb, revealing a fundamental dichotomy: first order Kerr/Faraday effects, governed by the antisymmetric optical conductivity, are odd functions of the Néel vector, while second-order Voigt/Schäfer-Hubert effects, determined by diagonal dielectric anisotropies, are even functions. Quantitatively, the Kerr rotation angle reaches up to ~0.55 mrad, the Faraday rotation up to ~6.9×10^5 mrad/cm, and the Voigt rotation up to ~10^6 mrad/cm, with their angular dependencies following distinct symmetry patterns. For the spin Hall effect, the time-reversal-odd (T-odd) and time-reversal-even (T-even) contributions to the spin Hall conductivity coexist and are of comparable magnitude (~10^2 hbar/e S/cm). In the ground-state Néel configuration along the c-axis, the T-even spin Hall conductivity reaches 265 hbar/e S/cm, while the T-odd component is 85 hbar/e S/cm, corresponding to charge-to-spin conversion efficiencies of 1.63% and 0.52%, respectively. Notably, reorienting the Néel vector not only modulates the transverse spin Hall components, but also activates longitudinal spin-current—charge-current configurations, which are strictly forbidden in the conventional spin Hall effect. These results establish a comprehensive, symmetry-governed framework for the Néel-vector dependence of magneto-optical and spin-transport responses in CrSb, offering a multi-dimensional response spectrum for probing the Néel vector direction.