Is a question "What is your body figure" grammatically correct? or "What is your body sizes?" I think this one is wrong. Which one is better?
Well, it's grammatically correct, but semantically odd. A more natural phrasing would be, "What is your body type?" This is, in fact, a rather common question in bodybuilding contexts, women's magazines and websites, and health forums, and is the way I'd recommend asking about this topic.
"What is your body sizes?" is grammatically incorrect because sizes is plural but is is singular. "What is your body size?" would be better, and is still more natural than "What is your body figure?" Also, "What is your dress size?" is a common enough question among women (if they know each other well enough to ask about such things).
Note that body type and body size are asking for different kinds of information, and both can be highly context-specific. For example, to a bodybuilder, body type means ectomorph, mesomorph, or endomorph. To a fashion-minded woman it might mean any number of things—here's a list of twelve different types. Body size might mean dress size, height, or weight, depending on the context.
I actually think that neither is very natural-sounding. A "body figure" could be redundant, as they might be considered synonymous. Also, "body sizes" makes it sound as if every body has multiple sizes. I would instead suggest:
What size are you?
What is your size?
When you ask someone this, they will infer the context. Are you in a shoe store? They'll give their shoe size. Are you selling them clothing? They will give you their clothing size. Note that if you are asking for a specific clothing item size, like for a pair of pants, you might want to say:
What pants size are you?