1. An adverb clause is a type of a subordinate clause. This means that it cannot exist on its own - it needs to be a part of a larger sentence in order to make sense. An adverb clause needs to have an adverbial function - this means that it should answer the questions why, when, where, etc.
2. The adverb clause here is - until his arms ached.
3. The adverb clause here is - once they saw her car turn the corner.
4. The adverb clause here is - When the storm started.
5. The adverb clause here is - while being taught to bake cupcakes.