Did it evolve from the beginning to the end?

In a matter of speaking; yes. While the basic strategy always remained the same; turning movements, deep raids into the rear, etc. How they went about doing so changed gradually as the war went onwards; losses, changes in equipment, a less 'regular' appearance and behaviour overall colored how they operated as the war went on.

Did cavalrymen use swords, or multiple pistols, or both?

Both; and very much dependent on the formation, especially for the irregularly equipped Confederates. Shotguns of various varieties were also not uncommon; and as the war went on many units began to have no sabers whatsoever - feeling them cumbersome and not suited for this new mode of warfare. Carbines were also abundant, and generally of an inferior or outdated quality to their Union counterparts. The Confederates would often dismount to fight, and saber or pistol charges are few and far between against enemy infantry.

Were riders from all socio-economic classes or did they come from, primarily, southern aristocracy? Or the poorer classes?

Oh my Goodness, without a doubt of all economic classes; and we have enough photographic plates of troopers before going off to war to prove this. The South had two things in great abundance: Horses for travel, and persons able to ride them skillfully. The Confederates actually had an excess of cavalry volunteers because most persons had the mount and ability to join such a regiment. The Confederate system of remount, was, however, often dependent on private income. If your horse was killed, or became unfit, and you could not purchase a replacement, you were usually drummed out of the regiment and into an infantry outfit. I digress however, the bottom line remains that a Confederate Cavalry regiment would get all sorts.

Did the either side employ lancers? They were widely used in Europe, but I have never heard of them in an American context,