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A critical exponent describes the leading singular power of an observable in a specified scaling limit. The order-parameter critical exponent describes the zero-field ordered branch; the magnetic-susceptibility critical exponent describes response to its conjugate field; and the critical-isotherm exponent describes response at the critical temperature. They are found in the Landau approximation by minimizing the potential and differentiating the resulting equation of state, as calculated in the question's root solution. For a leading $M^{2n}$ stabilizer the same calculation gives $M\asymp (-r{)}^{1/(2n-2)}$, $\chi \asymp r^{-1}$ and $M\asymp h^{1/(2n-1)}$. Thus $\beta =1/(2n-2)$, $\gamma =1$ and $\delta =2n-1$. Beyond the Landau approximation, the renormalization-group relevance exponents and anomalous dimension determine the singular powers; Question 2 derives their relations. The critical exponents refer to specified paths, and tuning to a higher multicritical point requires eliminating its lower relevant perturbations.