An Exponential-Log Growth

Let $f(x) = e^{ax} - 1 + \ln(x+1)$.

1. If $f(x)$ is increasing on $(-1, +\infty)$, find the range of possible values of $a$. 2. If $0 < a \leqslant 1$ and $x > 0$, prove that $f(x) > 2ax$.