What is the reason for the 'På" before menuen? It is not used at all in the sentence, but does it need to be there to make sense?
No. it doesn't have to be there. "Kokken har ændret menuen" is also perfectly acceptable. The only difference is very subtle: "Ændret på" is used when it's not a huge change; maybe the cook substituted one of the meals on the menu with something else. Without the "på" it would sound like she/he did a complete change of all the things on the menu.