I'm not exactly certain as to the minimum age one was required to have attained in order to be elected king of the Romans. Historically, I know that Heinrich IV was crowned King of the Romans during his father's lifetime at the age of three and in the seventeenth century you have Leopold I having his eldest son Joseph I elected king of the Romans at the age of eleven (though he was an adult by the time he succeeded as Emperor-Elect).
I believe that under Imperial Law, the only requirements for an Emperor were that he be at least 18, a layman and of noble birth (four grandparents). What's interesting here is that this criteria is outdated in assuming that the Imperial title is not automatic--I'm not sure how it would have been applied after the papal bull issued by Julius II in 1508 allowed the King of the Romans to automatically assume the title 'Emperor Elect'. I do know that when Joseph I was crowned King of the Romans, he took the coronation oath but was required to promise to renew it after attaining his majority (if this sheds any light on the question).
As for a regency, this was codified and provided for in the Golden Bull. In the case that the throne was empty or the King or Emperor was under age or incapacitated, authority was exercised by the Imperial Vicars as joint regents. These were the Elector Palatine and the Elector of Saxony, who had authority over the regions of the Empire under Franconian Law and Saxon Law respectively. I think that the Duke of Savoy was the titular vicar in Italy, as well, and I believe that Bohemia was specially privileged to be autonomous under its king (or its own regent, if the Emperor in question was also King of Bohemia).
The power of the Imperial Vicars technically lapsed as soon as the Emperor swore his coronation oath as a major. I also remember reading somewhere that if the new Emperor did not ratify their actions ex post facto, they would be null and void.
Edit: Also, there was a bitter dispute between the two main branches of the Wittelsbach family (i.e. the Electors Palatine and of Bavaria) concerning who had the right to act as Imperial Vicar after the end of the Thirty Years' War. This wasn't solved until some 100 years or so later, when the two branches agreed to alternate holding the title.
Hope this helps,
Amitiés,
Endymion
Yeah, I knew about the age requirement to become Emperor, but it seems to muddle the situation further as Constantine has pointed out designated heirs who were elected King of the Romans below the age of eighteen, with being granted that title basically meaning there would be no election as the King of the Romans automatically succeeded as Emperor upon his death. In a case like that, I wonder if that requirement that he be eighteen simply be dispensed with: after all, getting elected as King of the Romans is basically saying "Alright, we will accept you as our next Emperor."
Well that is a very interesting question. I looked it up and the youngest I can find was Holy Roman Emperor Joseph I, who was elected at age 12. Ans I think Emperor Henry VI extracted a promise to elect his son Frederich King/Emperor when he was, what 2, but that fell threw. So there doesn't seem to be an age limit on the election. But how young are we talking? 12? Younger? Older? It truly depends on the age.I think if he's at least 10 then we could see him already electing King, becoming Emperor immediately after his fathers death. If he's like 7 or younger, we might see something that happened with Henry VI. His brother Philip was elected Emperor while his son Frederich succeeded as King of Sicily.
As for the Regency, well going by the Austrian/Imperial Habsburgs, they controlled the Austrian Crownlands, Bohemia and parts of Hungary. So the Dowager Empress would govern these territories. I assume that she would also exercise official power over the Empire. Or we could see the Emperor's next oldest brother governing instead. Again it really depends on the situation. BTW, I don't think that the Arch-Chancellor really had any authority. By that time the title was divided among the Electoral Archbishops with the Archbishop of Mainz being senior. I'm not sure how much control the Emperor had over the Empire in that time but I would guess that it would be governed the same as it was before the Emperor's death. The Empress Regent/oldest Archduke would head the Regency council, with the child Emperor succeed. Though if a new Emperor besides the young son of the Previous Emperor was elected, then the situation gets very interesting. Does this Archduke control any territory or does he live in Vienna? Does he have children? Will he allow his nephew to succeed him or will he try to implant his own line onto the throne? If he lives in Vienna I think it would be understood that he's a Regent with a fancy title. If he rules say Inner Austria, or Further Austria then it gets very interesting..... yes very interesting indeed. Can you say Habsburg civil war

?
Seems I missed one then! Seeing Ferdinand IV elected at seventeen didn't seem too much of a stretch IMO, but seeing that someone was elected as King of the Romans when they were twelve helps out a lot of more, as it at least shows
some precedent of young heirs being elected to the title. Being King of the Romans was an empty title, much like the Prince of Wales or the Dauphin of France, but in a way it's also more important as it's a source of stability so to speak, that when his father dies the King of the Romans will succeed as Emperor without any fuss.
Yeah, the Arch-Chancellor came off the top of my head, but you're right. Most of those titles (Arch-Chancellor of Germany and Italy, Cupbearer, Treasurer, Butler ect) were all pretty empty titles and meant nothing. Even the Marshal of the Empire seemed to be merely symbolic (that is, the Arch-Marshal, not the
Imperial Field Marshals such as Prinz Eugene of Savoy).
This is actually a question I'm curious about as I'm considering using it as a potential situation in my timeline,
The Prince of Peace. The Habsburg Emperors rule over the Burgundian inheritance, Bohemia, and Austria proper, and are the main line, or 'Burgundian' Habsburgs. The 'Austrian' line rules Hungary and Croatia, but died out, being ruled by the last Austrian Habsburg, Mary, who was elected by the diet and fought against Imperial forces trying to claim the whole of the Austrian inheritance. She was able to keep the Kingdom of Hungary but lost Austria proper and Bohemia, and is married to a son of the French King, the Duke d'Orléans to be exact.
As for the age... I haven't quite decided yet, as I tend to change birth and death ages a lot before settling and writing the chapter. He'd be fairly young though, probably somewhere between 6 to 8, possibly nine. Looking over his family tree I have drawn up, he has no surviving uncles, but I think he actually will have an uncle in his family for extra drama, as mentioned, someone ambitious who possibly lived in his brother's shadow.

Even more interestingly (in a Chinese sense), this young Emperor's mother is the daughter of Queen Elizabeth and her husband, Frederick of Simmern, and the woman is a lot like her mother in many aspects... so definite regent material.
