As far as being one unit goes, since the adjective matches endings with its noun, they are separate units really; but under an important umbrella.
Sort of depends on what level of resolution you look at the sentence, because some times you could consider the sentence just two parts - subject and predicate. (or maybe break it up all the way to the word, or syllable or further)

I would say that the best way to look at it is that adjectives are separate, yet necessarily subordinated to their noun.

As for why the adjective is separated by word order, that is another fantastic aspect of Russian.

For example: to make out of snow
It is (made out of snow).

The woman is (made out of snow).

*The (made out of snow) woman said to me,....
The woman, (made out of snow), said to me....

For English, adjectives/participles that have a specifying prepositional adjunct can only be used as predicates. (or they can be offset in an inner clause like the last example)

In other words, the phrase "to be made out of snow" doesn't survive the form-transformations into all forms.
All of this is not the case for Russian.

You can imagine prepositions (среди, для) as being an opening box that only closes once a noun of corresponding case comes. A lot like parentheses

( ..................(............).................. ...)
среди..........для.....шаурмы....... .....ингредиентов

This only really happens though when the first preposition gets one of that noun's adjectives to "hold its place in line". So there's never going to be two prepositions in a row or anything.

для шаурмы as a unit is a prepositional phrase, or a (prepositional) adjunct.