The following is taken from $\textit{Categories}$ by Horst Schubert
Definition for Pullback
Let $f:A\rightarrow C, g:B\rightarrow C$ be two morhisms with the same codomain. A $\textit{pullback}$ (also$\textit{cartesian square,}$ or $\textit{fibre product}$) for the pair $(f,g)$ is a commutative rectangle
$(1)$$\quad\quad$$\begin{array}{ccccccccc} P & \xrightarrow{r} & B\\
\small {s}\big\downarrow & & \big\downarrow\small {g} & \\
A & \xrightarrow{f} & C
\end{array}$$\quad\quad$ $g\circ r=f\circ s$
with the following property: if $u:D\rightarrow A, v:D\rightarrow B$ are morphisms with $f\circ u=g\circ v,$ then there is exactly one morphism $w:D\rightarrow P$ with $u=s\circ w$ and $v=r\circ w.$
Definition for Pushout
Let $f:A\rightarrow B, g:A\rightarrow C$ be two morphisms with the same domain. A $\textit{pushout}$ (also$\textit{cocartesian square,}$ $\textit{amagalmated sum,}$ or even $\textit{fibre sum,}$) for the pair $(f,g)$ is a commutative rectangle
$(2)$$\quad\quad$$\begin{array}{ccccccccc} A & \xrightarrow{f} & B\\
\small {g}\big\downarrow & & \big\downarrow\small {s} & \\
C & \xrightarrow{r} & Q
\end{array}$$\quad\quad$ $s\circ f=r\circ g$
with the following property: if $u:B\rightarrow X, v:C\rightarrow X$ are morphisms with $u\circ f=v\circ g,$ then there is exactly one morphism $w:Q\rightarrow X$ with $u=w\circ s$ and $v=w\circ r.$
For the definitions of Pullback and Pushout, I have two quick questions.
(1) For the case of Pullback, there is often the phrase "$s$ is a pullback of $g$ along $f$, $(s,r)$ is a pullback of $(f,g)$. But for the case of pushout, is there a similar verbal description? If so, would it be something along the line of $s$ is a pushout of $g$ along $r$? or is it $s$ is a pushout of $g$ along $f$?
(2) How is the pushout diagram the dual of the pullback diagram. I thought all I need to do to get the pushout diagram is to simply reverse all the arrows in the pullback diagram? In many category theory text, when talking about the pushout diagram, all the book simply say is instruct the reader that the pushout is the dual of the pullback, and simply reverse all the arrows. To me, the pushout diagram is more than just reversing the arrows of the pullback diagram.
Thank you in advance