3 1/3 isn’t a sum expression. 23 may be shorthand for 2*10 + 3, but we don’t say that 23 uses addition. There is no ambiguity here.

Double factorials are factorials that take double steps from n to 2 or 1. Semifactorials are factorials that use half of the numbers in the range, i.e. the same thing. The naming may not be the best, but there is no ambiguity or error in ratio.

!! is a single symbol, like == or ** in many programming languages. n!! is unequal to (n!)! because they are completely different expressions. There is no ambiguity.

I can’t see that you have shown that mathematical language notation is ambiguous.