I also think that the bullets were made of pure lead, perhaps sometimes covered with a metal cup at the top.

Full metal jacket and solid metal Bullets are made since the end of the 19th century, but I cannot find out until now from when such bullets began to be used in rifles for big game hunting. I don't believe that such bullets were loaded into BP cartridges. In all probability these bullets were used at the same time as NC-powder when this replaced the BP in many big bore hunting cartridges.