The correct answer is option 4: "The Chairperson and members of the Armed Forces Tribunal can be removed only after consultation with the Chief Justice of India." This statement is incorrect because the Chairperson and members of the Armed Forces Tribunal can be removed by the President of India, and there is no requirement for consultation with the Chief Justice of India.

Let`s analyze the other options:

Option 1: The Armed Forces Tribunal does have the power to adjudicate disputes related to the conditions of service of persons subject to the Army Act, 1950. This includes matters such as promotions, pay, allowances, and disciplinary actions.

Option 2: Findings and sentences of court martial can indeed be challenged before the Armed Forces Tribunal. The Tribunal functions as an appellate body and has the authority to review and modify decisions made by lower courts martial.

Option 3: The appointment of the Chairperson and members of the Armed Forces Tribunal does require consultation with the Chief Justice of India. This consultation ensures that qualified and suitable candidates are selected for the positions.

In summary, option 4 is the incorrect statement as the Chairperson and members of the Armed Forces Tribunal can be removed by the President of India without the requirement for consultation with the Chief Justice of India.