My question is, when do you more knowledgeable people think that the Noldor, Sindar, Edain, etc. started using battlefield formations? I would imagine that they didn't have any such thing when they first experienced battle. It's a stated fact that the Numenoreans had a type spear-shaped formation at the time of the Last Alliance. At what time in-between were formations invented? Do you think Orcs ever used formations, or are they too unable to trust each other for that to work?
So, in our story, we had the Fëanorians developing formation warfare more or less in secret while they are at Formenos. This was done, in part, to give them something to do, but also to give the audience something other than "Informed Awesomeness" to remember when we see the Fëanorians demolishing the numerically superior orc armies when they first arrive in Beleriand.
For the rest of the Noldor, I don't think they really start catching on until much later, maybe by the Dagor Bragollach. Simple formations like a wedge have been used since the bronze age, so coming up with formations isn't hard. The tough part is having an organized enough society to have disciplined soldiers who can hold those formations and form them on command. For example, the Celts often used formations on Roman armies, but they would often break up upon contact with the more disciplined legionaries. Also, the Romans were able to change formations on the fly, making them more adaptable on the field. I think that by the time we reach the Nirnaeth, the Noldor will have reached the level of the High Middle Ages, able to execute complex maneuvers with specialized units. This has to do with their longevity as well as their focus.
Men, when they arrive, will be used primarily as auxiliary skirmishers. Unable to devote as much of their population to soldiery as the elves, their ranks will be made up primarily of non-professional soldiers with minimal training. We likely won't see humans reaching very high levels of battlefield discipline until the second age.
One of the things we have realized is that there are some specific "dark ages" in Middle Earth's history. Not everyone is affected, but those who are not tend to live in sheltered enclaves. The first dark age takes place after the Nirnaeth. The Noldor kingdoms are scattered, leaving vast expanses of Beleriand populated only by semi-permanent settlements of humans. Numenor and the coastal kingdoms of the elves eventually rise up and form great cultures. Sauron's rise with the power of the rings weakens the elvish kingdoms, though, so a second dark age follows the fall of Numenor. There is another buildup to the Last Alliance, after which the kingdom of Arnor disintegrates, the kingdom of Gondor decays, and the kingdom of Lindon diminishes, forming the third dark age. This lasts more or less until War of the Ring and the Fourth Age.