Is a String with no parantheses considered having balanced parantheses?
This is what formal definitions are for...

That said, it makes the most sense to allow no parentheses. Roughly speaking, a string has balanced parentheses if every left parenthesis is "matched" by a right parenthesis (of course this is far from being a formal definition). If there is no left parenthesis, then everything is OK.

Once you accept that, there is absolutely nothing wrong about the empty string – it is a string like any other. In particular, it is a string over your alphabet with balanced parentheses.

One way to formally define your language is using a context-free grammar. While there are many possible grammars, here is one that tried to capture the "matching" aspect when scanning the string from left to right:

$$
\begin{align*}
&amp;S \to \epsilon \\
&amp;S \to xS \\
&amp;S \to yS \\
&amp;S \to (S)S
\end{align*}
$$