You really got to the heart of the matter with your questions. I'll address the materials choice first.
Lead is quite dense and soft with a rather low melting point and thus was the best material for making musket balls. Its softness would not damage iron and steel barrels, and could be molded easily into various shapes. Copper is about 20% less dense than lead, is much harder but still much softer than steel and in its pure form (C110 alloy) less ductile than lead and not nearly as easily shaped as lead. Cutting lead in a lathe is impossible where as cutting C110 copper is readily done, but its ductility causes these long ribbon like "chips" to be made which can tangle into a huge ball around the tooling in an automatic Swiss lathe damaging the tools and guide bushing. This bird's nesting is avoided by using a program in the lathe that cuts off the chip before they get too long.
As a bullet material copper has several advantages. It is hard enough to resist the enormous compression forces of bullet impacts on soft targets without splattering, so weight retention is very high (85-95%), whereas lead can and will splatter at high impact velocities. Weight retention obviously improves penetration. Additionally, with proper hollow point design, the C110 copper bullet can be made to petal, creating "blades" that can make use of the rotational motion and energy of the bullet imparted to it by the rifling. Once expanded, these blades are sharp, and act like a high speed cutter (rotating at over 200,000 rpm from a 1:10 twist barrel) liquifying the tissue it is passing through. This also aids penetration. Finally, the hollow point can be tipped, reducing meplat size and improving BC. With a properly designed and cut hollow point and tip the bullet will have much lower nose drag, improved BC and energy at impact, efficient transfer of energy to the target causing a large temporary wound channel, and extremely good penetration enabling quartering shots that damage more organs.
Harder copper alloys such as free machining copper, will make chips that break off as the bullet is cut, but the bullets made of this material don't petal well at all and have to have larger holes as meplats to reliably expand, which reduce BC and thus terminal impact energy. Their manufacturers have to design a petal shedding type design with petals that have enough mass that they travel radially away from the bullet path. They are touted as inducing more damage, but that claim comes from intuitive speculation since the weight of each of the shedded petals is only a few grains. Additionally, the retained weight of the bullet is less and the blunt lighter shank does not penetrate as deeply. The petaling design I have seen in hunted animals allows at least 32" of penetration in bullets weighing 150 gr and less and several feet in yhe heavier 338 Bulldozers. Manufacturers of petal shedding bullets try to compensate by increasing MV by adding multiple groves to the shank in an effort to reduce the bearing surface in contact with the barrel. The groves, though, significantly increase skin or surface drag, further reducing BC and ultimately bullet impact energy. Our testing has shown that the increases in MV due to the groves is not large (30-70 fps or so), and when one factors in the difference in drag, the higher BC bullet will make up the difference in speed within 100 yds with the higher BC bullet passing the lower BC bullet for the duration of the flight. These differences in BC of bullets of the same weight can be large enough that by 500 yds the higher BC bullet can retain 45-50% more energy.
This answer is getting rater long, so I'll save a discussion about bullet groves for another time.