"I read the menu and eat the cake."
Translation:Tôi đọc thực đơn và ăn bánh.
You are right. The answer with "cái bánh" should be accepted. However, some phrases like "eat bread, eat cake..." in Vietnamese usually (if not all) does not involve a specific "thing". If possible, I can change this sentence to "I read menu and eat cake" if it sounds natural in English in order to match with the Vietnamese answer.
No, just cake. Bánh by itself doesn't literally mean cake. It refers to a very broad range of baked or steamed things you eat, and can be sweet or savory: bread, cakes, cookies, dumplings, crêpes, spring rolls, even noodles and rice paper. All these have different names: bánh + X (bánh mì, bánh xèo, bánh tránh, bánh bao). The type of bánh that a westerner would call a cake (like a birthday cake), I believe is called bánh kem. So yes, literally a cream bánh, I suppose referring to the frosting.
I just found this. I hadn't thought of it, but it does seem that a bánh is basically anything made with any type of flour: https://en.wikipedia.org/wiki/B%C3%A1nh