1) Game engine does not allow capital-less factions so it has to be something. Based on the current region list for HRE I think the Frankfurt will be the capital as it was the only seat of the Reichstag (besides Regensburg) we include as a settlement. Nearby Mainz (former settlement, now PSF) was also seat of Reichstag at some occassions so it would support it as well. The Emperor's residence is a tricky thing as it changed constantly and even Prague during Luxembourg era was not supposed to be permanent capital as Charles IV started massive building in Nürnberg in order to make it Reich's capital (never realized though, familiar, isn't it :-)). Player will have option to change his capital to whatever would be his liking, AI does not do that willingly. Currently we don't plan any specific features for HRE's current capital but it may change when we get to faction specific features later.
2) HRE will use Teutonic family tree from Kingdoms which means there is no family tree and the strongest general becomes the Emperor. The slight problem might be that despite the title was not hereditory the family influences played major role in the process and it later effectively became hereditory (since Charles IV. until HRE was dissolved it was pretty much in reality hereditory title!). We hope to simulate this via dynastic traits boosting stats required for becoming the Emperor. The second part of the question, what will happen, is directly based on the stats of the new emperor. If his authority is high enough he will succeed flawlessly. If not civil war and antiking will happen. Both features have been already presented, see
Previews and Promotions.
3) ERE Emperor will have contemporary title in Greek transliteration which I don't know right know. Certainly not Emperor, definitely not Holy Roman Emperor, unlikely Caesar.