You could say either one. I don't hear soup to nuts as often as I hear from beginning to end, but they are indeed interchangeable.

Although Wikipedia says that it is an "American English idiom," as a U.S. native speaker I have _almost never_ heard it used and I have never used it myself. Don't use it. Understand it if you hear it, but don't use it. I would guess that _many_ U.S. native speakers don't even know what it means. Just say "from beginning to end" or "from start to finish."

No, they are not interchangeable because soup is your first course in a meal and the nuts your dessert. Meaning from beginning to end.