My boyfriend's daughter is a small, short 9 yr old. she eat restaurant food and something sweet at least 5 days a week. is this an okay diet?

Restaurant food: Both balanced, healthy diets and high calorie, high fat, nutrient poor diets can be had at home and away from home. Small portions of sweets can be a part of either diet. Guidance for good choices can be found at ChoosemyPlate.gov - pick half vegetables, quarter grains/starches and quarter protein, along with a glass of milk to approximate.

So much for the: case that a hi-fat diet leads to growth. (This was introduced to explain why the average height in Japan is increasingly proportionate to the introduction of junk food.) You can eat healthy foods at restaurants, you just have to work at it a little harder, unless the restaurant specializes in healthy food. Sweets have to be balanced with protein for absorption, but probably aren't great.