Are the congregants obligated to sit as the sick Imam sits, if he is not sitting upright during the Tashahhud and between the two prostrations, in accordance with the Hadith: "Indeed, the Imam was appointed to be followed..."? And is his incorrect sitting posture in these positions binding upon the congregants?

If the Imam is ill and unable to sit upright between the two prostrations or during the Tashahhud, the congregants are not required to follow him in that posture. Instead, they should sit in the prescribed manner. This is not considered a breach of following the Imam. If the Imam omits a Sunnah whose performance by the congregant does not result in a significant deviation, such as the Jalsat al-Istiraha (resting posture), the congregant should perform it, because the discrepancy in this case is minor.