= Solution
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.
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