Finding the minterm expression of F + G
Here is my interpretation of your notation. The function $F = m(0,4,5,6)$ is in fact
$$ F = (x \land y \land z) \lor (\bar{x} \land y \land z) \lor (\bar{x} \land y \land \bar{z}) \lor (\bar{x} \land \bar{y} \land z). $$
(Perhaps positive and negative literals are switched, and possibly I am reading the bits in reverse order.)

The notation $F+G$ just means $F \lor G$. In that case, $m(S) + m(T) = m(S \cup T)$. Similarly, if $FG$ means $F \land G$, then $m(S)m(T) = m(S \cap T)$. Finally, the negation of $m(S)$ is $m(\bar{S})$. Basically, $m(S)$ is the function which is true on the truth assignments in $S$, so we can identify it with $S$. Boolean operations on functions correspond to boolean operations on sets.