Sorry are we talking about duels or battles?

Just before Sengoku Jidai and the widespread usage of mass Ashigaru formations, how would the fighting between mounted samurai archers play out?

Some smaller questions of the same time period:

• Was there a standardized code of conduct regarding fighting times/locations or did the peculiar circumstances naturally lead into constraints on the length, locations, and times of battles (ie most pre-modern armies didn't fight in the winter because it was a bad time for marching, foraging, etc.)?
• What roles did retainers have in these battles? I recall some users in a Shogun Total War thread mentioning that the samurai would not actually be moving too fast despite being mounted since they were constantly swapping weapons or being supplied with materials from their retainers, but I would like to hear more about this if possible.
• How many arrows would be exchanged combat? Would the arrows be cleaned up by retainers afterwards?
• How lethal was the fighting to the samurai, their retainers, and their horses? Would a samurai expect to lose a horse in a battle? Were retainers under great threat?

Your question is a good one but the problem is it needs a time period constraint. With the Muromachi period and before there are stories, plays and songs all about samurai combat, but they are like reading the Iliad and are to be taken with salt. The Tale of Heike is pretty fun to read if you have the time for it. So there are good accounts of stuff happening but there is honestly no real way to squeeze a time frame out of it.

By the end of the waring states period single combat is all but gone. It has been replaced by massed infantry and cavalry units. The spear and the gun are all important. So important in fact that one of the Japanese traditional martial arts is Jukendo or bayonet drills. The armor you have seen if its warring states period it will most likely be modified Portuguese or Dutch armor as they had really abandoned the lamellar armor towards the end. Most of the still existing lamellar armor is Tokugawa-Edo era reproductions, reproductions that are still like 400+ years old but still anachronistic.

Then you get to the Tokugawa period and you get armorless duels i would recommended reading up on Miyamoto Musashi. His duels would last anywhere from seconds to days depending on circumstances. He even wrote a book later in life the "Book of Five Rings". Its interesting but also ought to be read with a grain of salt.

I wish I could have answered your question better but there really isn't a good satisfying answer to your question. Each battle was different and kind of like watching mixed martial arts today, some bouts are over with a KO in seconds others will go the distance.

If your really interesting in reading up on samurai, I always recommend Steven Turnbull's stuff. Its easy to read lots of content and some cool pictures, and I don't care what anyone says pictures are cool to look at and really help in visualizing.