Not really, although some salad ingredients have been cooked. You would normally use the term "make a salad" rather than "cook a salad."
You can do. It depends on what kind of salad you are making; e.g a Waldorf salad would not require tomatoes.
baking
You can find a recipe on how to make a pasta salad in many salad cooking books. Visit your local bookstore like a Barnes & Noble and ask after their salad cooking books.
Cooking oil is purified fat from plants.
Neutral cooking oil, such as vegetable or canola oil, can be used for frying, sauting, baking, and salad dressings. It is versatile and has a high smoke point, making it suitable for a variety of cooking methods.
Making a salad.
It is not considered cooking, but it is considered a part of food preparation. There is a difference (hence prep cooks and line cooks).
Salad is something you can eat without cooking.
One can find some easy pasta salad recipes from a cooking channel (e.g. Food Channel), online cooking websites (e.g. Allrecipes), and a cooking recipe book.
it means you take your time making your salad.
A recipe for pea salad can be found at some cooking websites. A few to try are the sites for America's Test Kitchen, The Joy of Cooking, and The Food Network.
Celery is definitely a salad green