An ice maker should be a pvc line because it will need to be flexible. A copper line will work if the water source is directly behind the refrigerator, but if not then you will need a flexible line to reach from the water to the refrigerator.
Oh no, definitely not pvc. Your best choice would be the copper tube. There is one other alternative and that is the liable rubber-like tube, it is like the same one that is used inside the fridge to distribute the water.
It can be either type, but they are generally made of flexible copper tubing. You can also use flexible tubing made from other materials. The advantage of the copper is that you can cut it length, while the other types generally come in fixed lengths.