Is the sum $f+g$ of two one-way-functions a one-way-function?
The answer is no.

Given $f$ one-way, consider $g(x) = -f(x)$. $g$ is then also one-way, because inverting $g$ would imply inverting $f$.  In particular, supposing $g$ is not one-way, one can invert $f(x)$ simply by negating it and applying the inverter for $g$ (and the success probability is even equal).

In this setting, $h(x) = f(x) - f(x) = 0$ is not one-way as it can be.