Given ?1 and ?2, how do you calculate ?3 and ?4 after shortening the line segment by equal distance on each point?

Suppose distance between points $P,Q$ be denoted by $d(P,Q)$. Then you can find $d(P_1,P_2)$, call it $D$.

$P_3$ divides the segment $overline{P_1P_2}$ internally in the ratio $X:(D-X)$, so you can use the section formula $$ P_3 = dfrac{(D-X)P_1+XP_2}D tag{1}$$

and $P_4$ divides the segment $overline{P_1P_2}$ internally in the ratio $(D-X):X$, so $$ P_4 = dfrac{XP_1+(D-X)P_2}D$$

Note: If $P$ has coordinates $(x_P,y_P)$ (assuming you are working with $2$ coordinates, it works for any number of coordinates), then for $P_3=(x_{P_3},y_{P_3})$, $(1)$ means "apply it to each coordinate of $P_2$ and $P_3$", i.e. $$x_{P_3}=dfrac{(D-X)cdot x_{P_1}+Xcdot x_{P_2}}D\ y_{P_3}=dfrac{(D-X)cdot y_{P_1}+Xcdot y_{P_2}}D$$