No. The test for inability is explicitly described in the amendment. Congress is invoked to resolve disputes about the outcome of the test, because while the test is clear, it is not immune to dispute.
Certainly. Likewise, "made to pass the test of ability under duress" would fall under the "unable" category.
But the two questions are very different. "Is the president unable to act in the role, despite appearances?" is a much narrower question than "is the president acting in the role so badly that he should be removed?". Thus, since both questions require two thirds of Congress to support the desired outcome, impeachment is a much better fit for pursuing that outcome. One obvious reason this is so is that for the impeachment process, Congress doesn't have to explore the President's inner motives, only the external results. If the President is behaving badly, Congress can impeach him on that basis alone. If it's a 25th Amendment dispute, Congress has to actually answer the question of mental health, instead of simply examining the outcome.