I completely agree with Farry's answer.
As for the first question:
Is this correct for "Ask to see the menu": 要求看菜单
It is correct.
Is there a better or another way?
It depends on in what situation you want to use it. Colloquially, I would say "我想看一下菜单"/"我想看菜单"; in written language, 要求看菜单 is fine.