Several first-time player questions.

[Omanes Alexandrapolites]

I've noticed people talking about their general being low on health at some point in the battle, or noticing that their archers are running low on arrows.... I can't find a way to keep track of things like generals health, or archers ammo... ?

Archer's Amo can be monitored using the blue bar at the bottom of their unit card:

As far as I know, general's health and number of hit points cannot be monitored during battles. You can look at his traits prior to the battle though, and use them to work out his overall hit point levels (two is the base number of hitpoints, while certain traits add or subtract from the number).