Confederate Calvary under Forest carried only shotguns of carbines, only his personal guards carried sabers, towards the end of the war both sides Calvary ceased carrying sabers in favor of carbines because it's not that easy to run when dismounted with a saber hanging from your hip. Also the age of the magnificent Calgary charge ended at Waterloo, any charge like that during the civil war would be slaughter. In reply to your sharps rant, there were regiments in the union army that carried colt revolving rifles and Henry's, the Bucktails of Gettysburg fame carried sharps rifles, not carbines, and the main unit to carry sharps rifles were the US sharpshooters. Also if you read, you'll find that confederates, who used the whitworth, ditched the hexagonal bullets in favor of standard miniès because you can't really import special bullets for i high cost when your coast is blockaded. One rebel Calvary regiment carried lances, used them once, got slaughtered, then proceeded to use them for firewood. Also melee in the civil war didn't happen that much, that's why there are so many casualties, both sides would stand and blaze away at each other hours.
PS. In reply to the two types of Calvary you say "long range", ever hear of the mounted rifles and the mounted infantry?