problems with phrase structure trees

[der.schut]

You are perfectly right
and i think you will not correct homework either but i´ll try nevertheless. could you just say if it is right what i found out?that would be a great help.
my solution is:

1) "S: (Aux Are) + (NP you) + (VP interested (PP in (NP the (AP human) brain))))?"

2) "S:(Aux Would) + (NP you) + (VP like to conduct(does it belong together as one verb?) (NP research (PP into (NP the workings) (PP of (NP the brain))))) [Conj and] (VP join (NP an (AP enthusiastic, international) group (PP of (AP top) researchers)))?"

3) S:(NP The Master´s programme (PP in (AP Cognitive Neuroscience))) + (VP is (NP a (AP multi-disciplinary) programme) (VP?what is "closely involving" in this sentence?a whole VP? (AP closely) involving (NP scientists (PP from [NP(NP(AP various) faculties)) (Conj. and) (NP research institutes (PP on (NP campus)))])), + (Comp./subclause?: who (VP come (PP from (AP all) (PP over (NP the world))))."

4) "S:(NPThey) + (VP are (NP all(is "all" a noun phrase?) (PP of (NP(AP great international) standing))))."

5) "S: (NPThey) + (Aux will) (also? i think it´s an adverb but i don´t know where to put it) + (VP supervise (NP(NP your (AP practical) training) (Conj.and) (NP the writing (PP of (NP a Master´s thesis (PP in (NP the (AP second) year))))))."

[Blakist]

in the first example the tree should consist of S: NP- VP
[interesed in] VP [(in the human brain)] PP but connected to the VP