Translation:Is the milk in the fridge?
You don't have to have a measure word when you are talking in general. Only when you are measuring. Measure words go with numbers. Also it has nothing to do with whether it is food and drink: measure words are needed when talking about any specific quantity of anything.
我要买一本书。 I want to buy a book (i.e. One book)
Compare with general talk of books:
你经常买书吗？ Do you often buy books?
Your sentence is different because you are asking if there is a glass of milk in the fridge.
Both "in" and "inside" the fridge are correct, clear and natural English depending somewhat on the speaker's region. In California I can say that "in" would be the norm, but I've been other places where "inside" would be common and even others where "ice box" would be used rather than "fridge".