If anything, "for help" and "to bake some cookies" answer the question "what" not "why". What did she ask her mother for? answer = "help". And what did she ask her mother to do; answer = "bake some cookies".
A "why" adverbial (or reason adjunct) would be:
I asked my mother for help because I didn't know how to make cookies. I asked my mother to bake some cookies because the larder was empty.
In those examples, the underlined expressions are 'reason' adjuncts (adverbials); they answer the question why I asked my mother ...