Option B is false. The conditional default probability over a very short interval $(t, t + \Delta)$, given survival up to time $t$, is approximated by $\lambda \Delta$ (or $\lambda dt$). The expression $F(t)/\exp(-\lambda t)$ represents the ratio of the probability of default by time $t$ to the probability of survival to time $t$, which is not the conditional default probability over a short interval.

Option A is true. As $t \to \infty$, the cumulative survival time $e^{-\lambda t} \to 0$, meaning default is eventually certain.

Option C is true. By applying the chain rule, the derivative of $F(t) = 1 - e^{-\lambda t}$ is $F'(t) = -e^{-\lambda t} \cdot (-\lambda) = \lambda e^{-\lambda t}$, which represents the marginal default probability density.

Option D is true. The derivative of the survival function $S(t) = 1 - F(t) = e^{-\lambda t}$ is $-F'(t) = -\lambda e^{-\lambda t}$, which is the marginal survival probability and is less than zero.