To answer your question, $(\sim A \& B) \to X$ always means "If $A$ is false and $B$ is true, then $X$ is true". It never means "If $A$ is false and $B$ is false then $X$ is true".
The jargon here is this: You are asking about the "relative precedence" of $\sim$ and $\&$. Whenever you have two operators, say $\sim$ and $\&$, you can write expressions involving them with complete parentheses:
- $((\sim A) \& B)$
- $\sim(A\& B)$
These mean different things, and both are completely unambiguous. But we can also omit some of the parentheses and leave it up to convention which of the fully-parenthesized versions is meant. In this case you are asking whether $$(\sim A\& B)$$
means (1) or (2). If the effect of $\sim$ attaches only to $A$, as in (1), we say that $\sim$ has "higher precedence" than $\&$; if instead the effect of $\&$ attaches directly to $A$ and $B$, leaving the $\sim$ to apply to the larger $A\&B$ expression, as in (2), we say that $\&$ has higher precedence than $\sim$.
The universal convention is that $\sim$ has higher precedence than $\&$, so your expression means (1), not (2).
This is analogous to the way that $1 \times 2 + 3$ always means $(1 \times 2)+ 3$, not $1 \times (2 + 3)$.