Yes, you remove them completely from the oil and let them rest a bit. Mostly the fries are baked in 'fat' rather than oil though. Besides this, the type of potato that is used is pretty important too, as its consistency will impact a great deal too. The potatoes we use at home are called 'bintjes', they are a bit 'flowery'.
Yes, when double frying you remove fries from the oil and allow moisture near the surface to evaporate so it becomes tacky. For oil any common oil works but saturated fats get fries crispier. Even oven roasted potatoes in ghee and can almost get a french fry crunch. Duck fat is next level. Obviously much slower than frying.