Does the papal seat within each respective church need to be located in a specific spot or direction or can/should it be placed within the altar to allow His Holiness to sit throughout the Liturgy?
If there is a general meeting with the congregation where His Holiness is giving the congregation a sermon (not during the Liturgy) followed by a general Q&A session, should H.H. be seated on his papal seat facing the congregation or should he be seated on a separate chair?
Does either of these situations change if there is a bishop enthroned in that diocese?
The patriarch/pope is an archbishop. The official throne is always located on the north side of the chorus platform and faces south. If there is a need, there may be other chairs in the sanctuary for His Holiness, the presiding bishop, or other metropolitans and bishops, but none of these are an official throne. These chairs, if placed in the sanctuary, face east in the direction of the altar.
A visible example, which many people have witnessed, was set by H.H. Pope Shenouda III, and is currently being followed by H.H. Pope Tawadros II. During the weekly addresses to the public on Wednesday evenings in the St. Mark Cathedral, the patriarch generally sits on a chair facing the people. Often, a desk is placed in front of him so that he may set upon it whatever his needs may be during this session, e.g., notes, iPad, laptop, questions from the people, glass of water, etc. This scenario is not an official or liturgical setting. Certainly, if he is visiting any church, everyone will make sure that the pope has the best venue, furniture, and accommodations, as best as possible. Although the pope can address the people from the throne, even during Vespers, he will be more comfortable to sit on a chair facing the people, and have a desk set before him for a general Q & A session.
The pope can use the official throne of a diocesan bishop, but a visiting bishop cannot use another bishop’s throne.