Intertemporal utility maximization through consumption
Hint : You can write down your Lagrangian and simply take derivatives according to $c^{o}$ and $c^{m}$. So, you will mainly have two first order conditions with a lagrange multiplier. After, you will combine these two equation to eliminate your lagrange multiplier, which will give your intertemporal optimality condition (so-called Euler equation). I don't write the whole maximisation problem but only Euler condition.

$$bu^{'}\left(c^{o}\right)=\frac{u^{'}\left(c^{m}\right)}{1+r}$$

The role of interest rate is quite evident. If your interest rate increases, the marginal utiliy of consuming when old decreases, which means that it is optimal to consume more when old. Intuitively, it is plausible, if interest rate increases, the opportunity cost of consuming today increases.

For the second question, when you try to find optimal level of education, you should take the derivative according to $e$. So, the lagrange multiplier cancels out, which mean that you find a somewhat static problem. You will have ;

$$h^{'}(e)=\frac{1+r}{w}$$

If wage is higher, marginal utility of capital is less, which means that the level of education is higher. So, if wage is high, there are more incentives to invest on human capital. You can make the inverse similar interpretation for the interest rate.