I never assumed that warriors and soldiers were entirely separate categories; soldiers are warriors within organised armies.
Physical strength is important in combat, but speed and especially endurance matter just as much and weapon skill is also very important.
In some parts of the world, like Arabia at the time of the early Muslims, duels to the death between commanders and champions preceded battles as their troops watched, with the aim of boosting morale in the winning side and weakening in the losing side as well as potentially decapitating the enemy army by killing its leaders. The Muslim champions usually won these duels and the resulting morale boost helped their armies to win an astonishing series of victories, along with the superb leadership and tactics of Khalid ibn al-Walid and other generals, who himself killed a big number of men in duels and was a huge champion wrestler. Apart from these duels, most of the period's armies fought in formations as everyone did who had leaders in possession of brains. Muslims used tight ranks of spearmen with archers behind and quick, mobile cavalry units.
The same habit of duelling before a battle was common among Russian druzhina and many other cultures I am sure you can mention...well, I hope you can.
Individual combat does not mean non lethal at all. Combat can be individual, a skirmish or a battle, and lethal or non lethal. These things are not really connected, although battles are usually very lethal.
Ah, battle casualties. Battle deaths on the losing side only reached more than half if the army was utterly routed and/or trapped. Deaths in the main phase of the battle, before one army ran away, were usually about 1 in 10. Most deaths happened in the rout. If both armies withdrew in order, no higher casualty rates than that could be expected, so surviving multiple defeats was perfectly possible.