In Option (1), the phrase "beyond all reason" means something is irrational or unreasonable, which is used correctly here.
In Option (2), "any reason for her resignation" is a correct use of the word "reason" as it refers to an explanation.
In Option (3), "there is little reason in your pompous advice" means there is little logic or sense in the advice, and this is a valid expression.
In Option (4), "to a reason" is incorrect. The correct phrase would be "listen to reason," meaning to understand or accept logical arguments.
\[
\boxed{1}
\]