Yo, shipmate. Manuals I can't help with as I'm not aware of any. Those commands for loading and firing a revolver are quite naturally similar to the nine times or steps in loading and firing a rifle musket. Thanks for that link, by the way, it's interesting.
As for our comrades in the Army, the majority of handguns were carried by cavalrymen. As their main weapon was the sabre, which was carried on the left side and grasped and drawn with the right hand, they carried the pistol on the right side, butt forward so as to grasp and draw it left-handed. Infantrymen weren't issued revolvers, and would have tossed them into the bushes after the first day's march in any case. Artillery drivers, the only mounted men in light artillery batteries, were issued revolvers, theoretically for shooting wounded or panicked horses.
Officers of all branches were left to provide their own sidearms and carriage for same, which was often a sword (carried mainly as a badge of authority), and if they opted for the extra weight and encumbrance of a firearm, it was like as not a small pocket model such as the Colt Pocket Model of 1848 or 1849, or a Smith & Wesson .22 caliber. I've read the main purpose of the pistol was not as a short-range weapon of last resort, but to prevent a battlefield surgeon from lopping off an injured limb.
Our shipmates used different, minimalist holsters, called "frogs". These only had to secure the revolver, not also protect it from the elements. These were worn on the right side, butt to the rear. If revolvers, cutlasses, pikes, etc. were issued to repel boarders, the belt, cartridge box and frog were sometimes not bothered with, as more pressing matters were usually at hand.
Now, nothing I've just said should be taken as being engraved in stone - one thing you can probably count on is that every one of the preceding "rules" was broken many times.
Training in shooting from horseback - I dunno (we need a "shrug" smiley). The most common shooting stance was one-handed, lateral (turned to the side) while standing erect. Of course, this was formal shooting or a dueling posture. In combat, you could expect to see just about anything, I suppose. I've drilled in repelling boarders while facing square to the rail, but I had a cutlass in my right hand and a revolver in my left.
Well, that's about all I can say with any real authority, and as I said, don't take it as Gospel. One of the cool things about reenacting the Navy is that you can get away with a wide variety of weapons and accoutrements, as long as they fit with the period and geographical area. Infantryman, on the other hand, is a breeze because you just do what you're told, it takes no thinking at all.