Regular sets have linear growth?
Is it true that the set $0^{n^2}$ is not regular because it does not grow linearly?


Yes, that's true. That follows from the pumping lemma as explained in the paragraph you quoted.


  Therefore, $a^{n^2} b^n$ ... is not regular?


Yes, that's also true for the same reason.


  Also, I know that $a^n b^n$ is not regular, but what about $a^{cn} b^{dn}$ for any integer coefficients $c$ and $d$?


The language $\left\{a^{cn} b^{dn} \mid n \in \mathbb{N}\right\}$ where $c$ and $d$ are fixed is regular if and only if $c$ or $d$ is equal to 0.