Question about sampling
Whether the signal is periodic or not is largely irrelevant to sampling. What matters is the bandwidth. See this answer: https://dsp.stackexchange.com/a/10339/11256

There are two main cases:


If the signal is aperiodic and of infinite duration (for example, Gaussian noise), then $N$ samples will always be insufficient for reconstruction.
If the signal is aperiodic and of finite duration, then in theory its bandwidth is infinite and it cannot be reconstructed from any set of samples. However, many practical signals tend to zero as $t \rightarrow \pm\infty$, and their spectrum also tend to zero as $f \rightarrow \pm\infty$. In this case, you can obtain a reconstructed signal that is very close to the original, and for engineering applications this is more than enough.