1. What will you have from the menu above?

- I'll have a cheese sandwich and a large Coke.

2. What will you buy from the menu above?
- I'll buy a cheese sandwich and a large Coke.

3. What will you eat from the menu above?
- I'll eat a cheese sandwich and a large Coke.

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What does #1 mean?
Does #1 mean #2 or #3?

They all mean much the same thing, assuming the menu is a restaurant menu and the food is for sale. All would be legitimate questions for a waiter/waitress to ask, with appropriate answers.