Alright, your explanation is fully correct, I will add to it though, to make it correct and give you more insight about the elements. Wind is one unique one, so listen carefully.
Wind element is one the 5 basic elements and some element which is truly unique. I am guessing you know what what gives birth to every element is chakra, so in order for wind to be born, while you manipulate your chakra you will make your chakra light, fast and free flowing. While you are manipulating it, think of wind itself. This of the rustling of the leaves, think of the wind hitting your skin, moving your hair. Then consider the destructive power of it, think of the strong hurricanes which can destroy entire villages in just a very short time. Wind is the element which can have both. Once you are able to create wind chakra, you will see very small sharp blades of wind, which make it up. there blades have enough strength to cut through almost anything. But they can even be very fast and free flowing. As I said, it has the power to be the most useful element in the hands of a great user of it. The nature of wind is not hard to control, and you can give it a better thought. Think about the relations with the other elements. Consider lightning to it...which is the most destructive element of all. Lightning different from any other element will bring sure death to anyone who is even gonna try to face it...Wind can stop it. Wind won't allow the destructive lightning to penetrate. And then you think about fire...how fire is strong against wind, but that isn't fully true. If you use both correctly wind will not be weak against fire, it would be a great combination, creating stronger fire, which will burn stronger, brighter and give it directions and forms. Wind is truly an amazing element and if you walk through the path of it, you will understand why i find it truly the most unique and useful element. The relations between the other elements are fairly simple. Wind is strong to lightning...it is a natural insulator, it doesn't let lightning sparks to go through. Wind is weak against fire. The oxygen in the air you use for wind, will fuel the flames and make them burn brighter and hotter. Earth has a unique relation. The very sharp tiny blades of wind, would be strong enough to rip the earth apart, so you can't make combos with it. Water is pretty similar to fire. In combos you can aid a water technique with wind to make it a lot faster, and give your attack even more speed.
Now onto shape and nature manipulation. What you said was of course correct. But I will try and give you a better understanding.
Shape manipulation is when you give shape to the chakra you release. Think about it. As you release chakra, you will try and create an image in your head, like a sphere...Then slowly you will fill that shape with chakra. But this sphere will even have a certain effect in chakra, it could be rotating, standing firm, solid ect....The sky is the limit. You can shape the chakra into anything you want even very specific shapes giving you a great weapon.
Nature manipulation is the filling half of shape manipulation giving you the chance to change the raw chakra into something else of either the basic 5 elements. When you do this, you will simply think of the element, and change your chakra according to that. For fire, you think of it as a super hot burning mass. For lightning you vibrate your chakra creating sparks, and for wind in this case, you make your chakra light, fast and free flowing.
Taking a deep breath, I look at my student and ask her.
Any questions so far?