Going between sheaves and slices

Question

(By sheaf, I mean a sheaf of sets.)

Let $X$ denote a topological space. If I understand correctly, there seems to be a way of turning sheaves on $X$ into slices of $X$, and vice versa. In particular, I think the following is true:

1. Suppose we have a slice $\pi:E \rightarrow X$ of $X$. Then if I'm not mistaken, the local sections of $\pi$ should organize themselves into a sheaf.

2. Conversely, suppose we have a sheaf $\mathcal{F}$ on $X$. Then the germs of this sheaf should organize themselves into a slice $\pi:\mathrm{Germ}(\mathcal{F}) \rightarrow X.$

Questions.

QA. Is this correct?

QB. If so, what is the usual notation for what I'm denoting $\mathrm{Germ}(\mathcal{F})$, and what's the precise way in which all the stalks organize themselves into a single topological space $\mathrm{Germ}(\mathcal{F})$?

QC. Are there any further basic facts about the relationship between sheaves and slices that are really essential to understanding what's going on here?