Question about violating the zero conditional mean assumption
If you introduce any sort of correlation between the explanatory variables $X$ and the error $\epsilon$ then the zero conditional mean may be violated. In your example, if you were to assign women their training time according to their age, then the exogeneity assumption breaks.

More formally, this last condition means

$$
\mathbb{E}[\epsilon|X] = 0
$$

If, wlog we assume $\mathbb{E}[\epsilon] = 0$, and there's a non-vanishing correlation between $X$ and $\epsilon$ then

$$
 0\not= \mathbb{C}{\rm ov}[X,\epsilon] = \mathbb{E}[X^t\epsilon] + \mathbb{E}[X] \mathbb{E}[\epsilon] = \mathbb{E}[X^t\epsilon]
$$

therefore $\mathbb{E}[\epsilon|X]\not = 0$