Answers and Explanations:
- were
- would have listened
- were
- would resign
If the CEO were...
This tests the formal subjunctive "were" for a counterfactual state. Because her nature is an ongoing, general trait, we use the past subjunctive ("were") rather than the past perfect. While "was" is sometimes heard in informal speech, "were" is the grammatically correct subjunctive form required in formal writing.
...she would have listened...
This is a mixed conditional. The condition is a general, ongoing state (If she were reasonable), but the result happened in the past (...she would have listened last month).
Furthermore, were she to propose...
This is an inverted conditional replacing "If she were to propose." "Was" is strictly incorrect in inverted conditionals.
...I would resign on the spot!
The condition talks about a hypothetical future event (tomorrow's meeting), so we use the standard conditional "would resign."