The Zulfiqar, or Ali's forked sword: It is said that one of Prophet Muhammed's companions, Ali, owned a forked sword. I searched for images, and I saw several different possible designs. Do historians or artisans have an accurate picture of what the Zulfiqar looked like?
Most likely no. Most likely Ali's sword was given some poetic description, but it may have just been a normal sword originally. Swords claiming to be the original, unless this has changed with new research, are later creations for ceremonial purposes (such as the Ottoman sword).
Did the Caliphate appoint/elect leaders? So I recently found this series of videos on Islam's history by the Caspian Report, a YouTube channel.
The first in the series covered the early history and the Rashidun Caliphate. Around the 1:00 mark alleged that the Caliphate functioned similar to a democracy, where the most notable members of the communities got together in a council and appointed the Muslim community's leader by a majority approval. The video explains that the disagreement between the legitimacy of Abu Bakr vs. Ali as to be a dispute due to this.
Now, I found this peculiar, in that I assumed that the Caliphate's leadership was a hereditary aristocracy, but I could be wrong. The comments section took issue with several claims in the video, such as sympathy for Ali as well as the statement that the East Roman Empire (Byzantines) planned on conquering the Arabian peninsula.
So in regards to this, how did the Caliphate in its early years typically appoint a leader? Was there a council/parliament/etc meant to act as a regulator or granter for the ruling Caliph?
The traditional story will change depending on who you ask. As Formless explained, some details are remembered differently. The reason for this is he, I, and many Muslims are from a Sunni background, while Caspian Report is most likely from a Shia background. Both sides keep their own traditions on the matter.
Partisan debates aside, the general point is true within traditional Islamic historiography: the Rashidun Caliphs were righteous because they were chosen by a tribal election council, while the Umayyads who replaced them are evil because they turned the caliphate into a dynastic title. From then on theoretical discussions on who should be caliph and how carried on, all the while the title passed on like a monarchy anyway. Each theological tradition holds its own specifications, but generally speaking Sunni tradition asks that a caliph be elected by representation of all Muslims, either by delegation of the people or by their ulama, and that he descend from the tribe of the Prophet. Candidates should be elected based on their personal virtues.
What most likely happened historically, however, was that the first caliphs did not call themselves as such. They were the Commanders of the Faithful, and the title Caliph was likely the brainchild of the Umayyad dynasts who looked to turn the nascent Arabian Empire into a state that paralleled the Byzantines, and where the Caliph was the equivalent of the Roman Emperor. Later on the new ulama class of scholars looked to seize that title and posturing away from them, and the two concepts of Caliph and Commander of the Faithful were combined to be one and the same by the time the Abbasids entered the scene. As for the early succession disputes between Abu Bakr and Ali? I very much doubt Ali ever stood a chance at being elected before the other three. Consider the succession laws of modern Arab monarchies - Agnatic Seniority. The oldest male relative is favored above closest male relative.
Abu Bakr was born 573 AD
Umar was born 577 AD
Uthman was also born 577 AD
And Ali was born sometime around 600 AD
Then lets look at their relation to the Prophet:
Abu Bakr was Father-in-Law through Aisha
Umar was also Father-in-Law through Hafsa (married to Muhammad after Aisha)
Uthman was the first Son-in-Law through Muhammad's eldest surviving daughter
Ali was Son-in-Law through Muhammad's youngest surviving daughter
Assuming Arabian norms on tribal leadership and patriarchy haven't changed drastically, we can see the clear hierarchy that would have shut out Ali easily in the first three elections, if they were elections at all to begin with and not a succession council vetting candidates through seniority as well as absolute virtues.