Of course copper was used as a weapon 4-5000 years ago, until they figured out to smelt different stuff. Spearheads and arrowtips have been found, but were they really used for war?
Never found any good info on copperswords, except for a very fine timeline, before bronzeworking was made. So in reality, maybe copper swords was used for this or that, but they certainly existed.
Hunter-gatherers used copper-weapons for sure, but it doesn't say they couldn't have been used in wars for a brief time of history.
And really, who cares? Don't we have enough weapons in Civ already?
I'd say rejiggering the current units would probably be better than adding lots of new ones.
I've suggested adding one new unit line up to gunpowder that is cheap, weak, and counters the spear line hammer for hammer, and iron simply isn't important enough I would say, and it is placed on the wrong units. The basic units of an era shouldn't require a resource, while siege and specific counter units probably should, but the specifics aren't for here.
As far as extending the early eras, simply adding new techs and putting some things in different places could go a long way. Move Walls and Stone Works to Cement, and National Epic to Alphabet (and change to Drama and Poetry leads to Writing leads to Alphabet) and maybe make it a requirement to found a religion. By flipping Writing and Calendar, you could add Law as a requirement for Theology and Civil Service (in place of Drama and Poetry), complete with Courthouses and probably something else (I'm making this up 100% on the spot). One could claim that Horseback Riding and Mathematics could lead to Sports.
That's 4 techs right off the top of my head to add to those early eras. Just adding a new building or two would likely help lengthen the early eras, and so long as there aren't too many empty techs (one or two would even be ok if the payoff for researching it or getting access to another tech is worth it, maybe Magnetism between Optics and Compass for very quick access to the Medieval era, for instance), but the combat in early eras would still need some work, but, again, that wouldn't require new units really.
However, G&K really did focus on the later eras, so maybe the next expansion will really flesh out those early eras too.