Greenery

Сan the word "greenery" be used as common name to parsley, dill, and and other such things? If not, what is the right word?

The word "greenery" refers to green plants, but is not specifically used for edible plants and herbs such as parsley and dill.  Rather, it emphasizes the fact that the plants are green.   Example:  I like to hike in the countryside where there is so much greenery -- trees, bushes, and grass.

Parsley and dill are examples of "herbs", which are plants which are used to flavor food, and which are often aromatic.

The word "greens" also might be what you are looking for.  "Greens" means green, leafy vegetables.  Examples:  kale, collard, turnip greens, beet greens, Swiss chard, spinach, cabbage, and lettuce.   Example of use:  A mother says to her son, "You can't get up from the table until you've eaten your greens."