Cavalary fighting style

Sorry if this was already covered somewhere here, but I couldn't find it. On another section of this forum I saw a thread named "surprisingly bad units" and there were some cavalry units there which were considered ineffective. Someone there said that actually everyone can wound a horse and cripple both the rider and the animal.

So the question is: how the cavalry was really fighting. Did they crash into the enemy and withdraw after their charge was spent? Did they stay and fight? If they were turning away and withdrawing, how could they avoid being decimated by the arrows and bullets fired at their backs? If they stayed, how could they protect their horses? This leads to another question - what was the role of the cavalry for non-steppe nations? Were they only morale breakers? Did they only disrupt the formation and let the infantry take over from there? Or were they used mostly for flanking and harassing?

Well, that's already a lot of questions, so I think I'll stop here.

Flanking, harrassing, screening, scouting, skirmishing, fighting other cavalry and chasing down routers in the main, since most cavalry was light.

Alexander's style of heavy cavalry use, to charge to the rear and flanks of engaged, and tired infantry required bigger, heavier horses trained in a particular manner. Which were more expensive and harder to come by.

There are several thread ere about this, mainly discussing about the charge. Write 'cavalry charge' in the search