Student or Learner
I know that sentences like IŽll take you up on that cup of coffee are very common. How common is it for natives to ask questions using this idiom, like Do you always take your wife up on her invitations? What questions would sound natural?
Not a teacher.
I don't use it that much, but other people do. It is just a matter of preference. You could use it whenever someone makes an offer of some kind.
You don't ask questions using this idiom, you make a statement about the actions that you are going to take, or have taken (I took him up on his job offer).