Q. 1. Can the Pope be removed from office? Let's say he is too sick to administer his position as the head of the Catholic Church, can he be removed?
A. 1. The answer to your question is "No!" The Pope cannot be removed from office.
According to Canon Law # 331, the Pope is the Supreme Pontiff. There is no worldly authority above him. He cannot be removed from office.
Can. 331 "The bishop of the Roman Church, in whom continues the office given by the Lord uniquely to Peter, the first of the Apostles, and to be transmitted to his successors, is the head of the college of bishops, the Vicar of Christ, and the pastor of the universal Church on earth. By virtue of his office he possesses supreme, full, immediate, and universal ordinary power in the Church, which he is always able to exercise freely."
The Pope can resign from his office, providing that this is done with a free will and he does so by informing the College of Cardinals of his intention.
Can. 332 §2. "If it happens that the Roman Pontiff resigns his office, it is required for validity that the resignation is made freely and properly manifested but not that it is accepted by anyone.
Canon Law # 187 states that anybody can resign from any ecclesiastical office for a just reason, so long as he is "sui compos." A person who is considered "sui compos" is one who has the ability to think for himself, and make responsible choices using his own mental power.
The opposite of being "sui compos" is one who is mentally disabled, unconscious, insane, or suffering from dementia. Such a person would be unable to rationalize what he is doing, and to take responsibility for his actions.
So if the Pope could not make a rational decision on his own, he would not be in a position to make the decision to resign. Nor would anyone have the authority to remove him from office because he is the Supreme Pontiff. This rule ensures that there will never be one or more in power who will overthrow the Pope by removing him from office for whatever reason. If the Pope does not resign with a free will, he will remain as Pope until death.
If the Pope becomes incapacitated due to deteriorating health, the status of the Papal Seat is as if the Pope had died or became "non sui compos". During such time, no major changes can be implemented in the governance of the Catholic Church because only the Pope has the authority to do so.
Can. 335 "When the Roman See is vacant or entirely impeded, nothing is to be altered in the governance of the universal Church; the special laws issued for these circumstances, however, are to be observed."