Preface: American Civil War and "the rest" (Franco-Prussian and Austro-Prussian primarily are two separate entities. They were two entirely different methods of waging war and need to be treated as separate cases. The Americans had a Jominian (a Napoleonic military theorist) understanding of warfare and thus attempted to replicate Napoleonic methods tactically. It failed horrendously. The rest of the West, basically, Europe, would have a style of war which swung much more in the WWI-side of the spectrum in their respective Austro-Prussian and Franco-Prussian Wars.

You're asking a lot of questions here so I'm not even going to really try and give some kind of definitive answer. When did men begin to "find cover" and do something reminiscent of "suppressive fire"? About the same time men were still "in rank and fire" and "unloading volley after volley". Light infantry became a "thing" in the mid 1700's and would be an integral part of European warfare in the Napoleonic Era where a light infantry body would win or lose battles at time. Wellington would at times make 1/3rd of his force skirmisher/light infantry forces which would decimate enemy formations; all which would be 'taking cover' and the like. Further, and this is just pre-post pettiness, Napoleonic warfare was more than just two sides lining up in an open field and unloading on each other until one side gave up. This is very important to know because having a strong understanding of Napoleon's tactics are necessary to understand America's in the Civil War, and, most importantly, why it didn't work and why it was faux-Napoleonic. In short, Napoleons tactics were to use combined arms to force the enemy to dedicate his reserves to the flank and thus engage the entire enemy force. He would then use his own reserves to smash into the enemy weak spot with massive columns in a final bayonet charge to crush the enemy with overwhelming numbers.

Let me make this clear as it's important: It was the cooperation between the infantry, cavalry, and artillery that locked the enemy in place through a delicate dance of maneuver and the reserves that decided the battle. The American Civil War was absolutely nothing like this but it attempted to, and now we get to what an American Civil War battle looked like. Whereas in a Napoleonic battle you'd have a mass of columns approaching the enemy and forming a line or staying in a column respective to the situation with cavalry advancing with the infantry and artillery batteries suppressing the enemy while skirmisher formations screen the enemy and pick them off, the Americans had just one of these components: the infantry bit. Their artillery was present but hardly as decisive as Napoleon (or his contemporaries) would use them. The Union never really had anything resembling real light infantry battalions and the CSA, while using them in small number, never really put them to use in mass as his European contemporaries were and as they were used in the Napoleonic Wars.

Further, and perhaps most deadly of all, rifled muskets along with advances made cavalry nearly useless. This is only compounded by the fact that America had no cavalry tradition whatsoever and thus what little cavalry they did have were dragoons (mounted infantry, essentially) and scouts. They had next to nothing to 'crash' into the enemy and be that decisive factor and what little they did had was useless in the face of rifled muskets which were accurate up to 350 yards and effective to 500. Last but certainly not least the Americans on either side were not keen on keeping reserves which, again, was completely against the entire principle of the tactics they were trying to apply.

What we get, in result, is an absolute bloodbath that we now know as the American Civil War and notable battles like Gettysburg. Pickett's Charge would have, with Napoleon, been accompanied with cavalry to add a decisive shock factor and to draw out the enemy reserves. Instead it was a colossal failure. In fact Pickett's Charge is a microcosm of ACW tactics as a whole. Justus Scheibert, a Prussian observer to the ACW, commented on his experience with witnessing a battle:

*"The nearer to the enemy, the more faulty the lines and the more ragged the first (line) until it crumbled and mixed with the skirmishers. Forward went this muddle leading the wavy rest. Finally the mass obtruded upon the point of attack. In a sustained, stubborn clash, even the third would join the melee. Meanwhile the usually weak reserve tried to be useful on the flanks, or stiffened places that faltered, or plugged holes. In sum it had been a division neatly drawn up. Now its units, anything but neat, vaguely coherent, resembled a swarm of skirmishers."*^[1]

This is really what ACW battles came down to. They were entirely indecisive as they lacked a deciding factor. Even infantry can be that factor with the right weapons but they just didn't have them. So the answer to what a American Civil War battle looked like was two massive blobs of infantry with 5-6 men packed into a square meter elbow to elbow and using modern, rifled muskets. They would meet, fire off volleys at each other and try to act with a column attack that was entirely unsupported by cavalry and only marginally so by artillery and without any skirmishing body to weaken the enemy. It would have been an absolute bloodbath and a chaotic mess. With totally amateur officers on all levels of command compounding this men just could not engage with the enemy. There are too many cases of a battalion attempting a charge and just stopping short and breaking down formation into just, as Scheibert calls it, a loose collection of line infantry who are now "skirmishers" who just charged the enemy and are now, short of them, just dissolving into random and uncontrolled fire. In response to this by the end of the war bloody campaigns of attrition like the Petersburg and Overland campaigns.

Really one of the biggest issues with the Americans was their insistence on using, at first, the Regiment (1500) as the smallest tactical unit and later the Battalion (800). One officer would lead these men and if he died the entire thing went to crap. There was no backup plan -- the entire regiment or battalion operates as one. It fights as one and dies as one. This was an incredibly Napoleonic way of doing things while, as our friend Scheibert will again observe, Europeans were already on the path out of:

"Prussian tactics freed (officers) to use their own minds... Liberated battalion and even company commanders could be the heads of tactical units, their own, and make them fight as right-thinking officers saw fit and as well-trained troops best could. The flexible line at the forward edge resembles a chain , then with detachable links under independent guidance. At crisis they can dismember into smaller and even the smallest units without disfunction... Our Prussian tactics thus gave our line officers energy, elasticity, and speed - to the entire army's benefit... Furthermore, diligent peacetime training provided our troops an abundance of formations, something to fit any circumstance."^[2]

This is a nice transition into the European style of warfare; something which is looking as I said more in the WWI side of the pendulum than the Napoleonic. What Sheibert just described is what is commonly referred to as an "infantry chain", that is, the gradual breaking down of infantry bodies into smaller tactically independent units. It doesn't matter too much if your Battalion Commander gets popped because your lieutenant or your colonel or whatever can just break off on his own and make his own decisions.This is the beginnings of squad based warfare that will be so prevalent in WW2 and contemporary warfare. Rather than operating in groups of 800 or god forbid 1500 you would see Company's and Platoons with men as little as 80-100 operating independent from the rest of the body.