what's the meaning of LOC(X[j]) = $L_0$ + cj in TAOCP's 5.4.1R?
The key observation may be each array element of X (regrettably called node by DEK, just as the nodes of fig. 63) representing one internal (round) and one external (rectangular) node of figure 63 with no discernible relation.
1&amp;2) Don't think so, for this formula it should suffice to take LOC(X(j)) as the location in MIX's linear memory of (the first word of) the jth element of array X of records of c words each (see 2nd paragraph above), a natural number from 0 to 3999. (Then, there is en.wikipedia.org/wiki/MIX)
3) yes, $cj$ is consise for $c * j$
4) $L_0$ seems to be the location of the first word of all the consecutive words representing Algoritm R's data structure
5) Those LOC()-expressions denote the locations of X's elements 9, 8, and 2, resp.
6) no relation I can see: $17$ happens to be $5 + P = 5 + 12$, the parent (external, PE) of which is (internal) node 8, coincidentally represented by the same element as (external) node 20, parent (internal, PI, used to be FI(/FE) in 1st ed.) of node 5 is 2, $14 = 2 + P$ happens to share the same element of X.