Does the author clarify further in the passage that 'complement' can be part of a clause?
To take your last, main question first, No, Prof. Eastwood does not make this clear in the snippet you provide. However, it may have been made clear earlier, or it may be made clear later, after Prof. Eastwood has laid what he considers an adequate foundation.
What is meant by 'other phrases, too' here? Does it mean other sentence elements, like complement? Or does it mean the types of phrases other than 'noun phrase' and 'verb phrase'.
It appears that Prof. Eastwood is building his introduction to syntax on the phrase, so I imagine that he means phrases of all types, and that he uses the term phrase in a fairly narrow sense. His approach is by no means universal in grammatical discourse; verb phrase, for instance, in many grammars denotes not just the few words will be but "the entire string of words governed (or headed) by a verb". Your quotation from Wikipedia employs 'verb phrase' in the latter sense. Traditional grammar, on the other hand, calls what Prof. Eastwood identifies as a 'verb phrase' simply the verb.
So as you can see, the matter is complicated by critical terminological differences; and we haven't yet even started to address what a clause is!
I am not acquainted with the Oxford Guide to English Grammar, so I cannot be sure; but it seems to me that Prof. Eastwood is trying to build your house from the ground up, brick by brick, rather than exhibiting its overall design first, and only then showing you where the bricks fit. I therefore suggest that you would do better to take his study in larger chunks. Read through an entire chapter to get a sense of his argument; then go back and reread, and perhaps everything will be clearer. If anything still baffles you you will at least be able to bring us specific, narrow questions we can handle within the 200-800 words of an ordinary answer.
Both sentences are grammatical. Even in the link, Swan's grammar book says "usually go in the end position" (emphasis mine).
Of course, the most natural way is
Vasya did this homework at school. :)
The passive doesn't seem all that natural to describe or talk about such an everyday situation.
But since you asked, the first one
This homework was done by Vasya at school.
seems more generic and therefore natural than
This homework was done at school by Vasya.
I have not bolded at school as in your originals, because in either sentence one can stress either Vasya or at school, or both, at least when talking.
In writing, the term that comes first (Vasya or at school) seems to get more stress if read without deliberately stressing a word.
Best Answer
It is normal to place longer phrases at the end of sentences.
This tendency is called End weight. It is not only seen in English, but in some other languages too.
Your sentence is a good example. The "original form" is relatively clumsy. The very short verb phrase "exists" seems to dangle at the end of a long and complex subject.
There is a solution, and that solution is the one used in the example. The "of" phrase can be moved to the end of the phrase, and in doing so it improves the sentence, by making it less clumsy.
See the linked website for further examples.