Is eating out considered a board expense (room and board subject) while attending college?

No. Not at all. That's an entertainment expense and not deductible as an education expense or education support expense by any means.

What about groceries?

The cost of food that can be claimed against 529 funds each semester can not exceed the cost of the school's meal plan for that semester.  It is not required, but highly suggested that you keep all grocery shopping receipts. There is one exception.

If the student was issued a letter by the school informing them that on campus housing was not available for the semester, then the cost of room and board claimed can exceed what the school would otherwise charge for the same. However, the costs claimed must be reasonable for the location. In other words, no $5000/mo penthouse suites and no steak and lobster for lunch/supper every day.

As for the letter from the college, that doesn't get filed with the tax return or anything. However, if the tax filer is audited by the IRS on what they might think are "excess claims", then you would need that letter to justify your claim for room and board being higher than what the school charges. Generally, you'll have a letter for each semester where the student was enrolled as at least a half time student for that semester.