At any moment if the president is impeached or dies the Vice President will be the next in line.
In Gothic architecture, there would always be a pointed arch and a ribbed vault, as well as a flying buttress. The entire place would have numerous carvings of great artistic value that would only point out even more how great of a building it would be, since it was one of the primary goals of Gothic builders, making things huge and imposing.
I would've enjoyed because becoming a master builder for such a project means that the government of the country trusts you to be skillful enough to create such a massive building with huge historic importance and this would only mean that they have you in high esteem and respect you. It would be something like the cherry on top of an amazing architectural career.
The big difference is that today's judgments have a legal rite. People should be judged with dignity, which was not always the case at that time, and condemnation must be evidence-based, which was not always respected either.
Another difference is that today there is no judgment based on supernatural situations, as was the case of the Witches of Salem. For a judgment made under the aegis of democracy, crime must have motives that can be substantiated. Finally, people who are tried today have a broad right of defense, which was not the case in the Middle Ages.
Because there was cheaper and faster transportation.