Basically, Nagato has the ability to use all 6 elements if he wants to. He could maybe even use 3 together if he's good enough. That's what the Rinnegan and the whole sage of the 6 paths thing does for him. As far as his puppet people: it's all up in the air. Either he can only use one special technique per puppet, or he builds them up beforehand to use techniques. For example, he would have to specifically set up a puppet that could absorb earth/water element chakra he gives off to use wood element technique.