How does structure or the use of the vegetated assembly influence the final design? Is this a decoration or an integral part of a larger building system?

What type of material are you using? Masonry? Bricks. Stones. And how plants grow on them and the need to maintain a subsurface. If it is not masonry, then it is most other materials. Wood, vinyl, metal, among others. And how plants grow on them and the need to maintain a subsurface.

What does decorative mean and how does this influence a wall design? Does this means its only there for its looks? What about when the wall is there only to perform a function and nothing more. Or should it also be well designed and attractive?

I believe that a vegetated wall or assembly can do both of these things. In fact it must in architecture.