Yes it does, however in this context it would not be used. There are a wide variety of courses to choose from. OR You have a diverse number of courses to choose from. There are many electives to choose from. There are lots of different types of electives to choose from. I personally would use wide variety or many they are quite natural. Diverse is more academic. Assortment is more of a mixture of things, such as clothes, shoes, food, furniture.In his cupboard there's a large assortment of clothes and stuff. The shoes come in assorted colours.

Yes, a variety. Perhaps even a selection, but that would make the sentence sound funny.

Yes.