Structure Dependency!?!?!?

[MIC85]

I have the following two sentences :

The boy who is sleeping was dreaming.
The boy who can sleep will dream.

if I want to make a question out of the first sentence then I should move the auxiliary of the top most sentence ( The boy was dreaming) to the beginning
(Was the boy who is sleeping dreaming?).
Now, is the following (who is sleeping) an embedded sentence?
And if it is, is who considered a complement?
Is the tree diagram of the sentence correct?

S = The boy who is sleeping was dreaming

NP = det.(The) + n. (boy) + CP (who is sleeping)

CP = c. (who) + embedded sentence ( NP + VP)

NP of embedded sentence = NONE

VP of embedded sentence = aux. (is) + v. (sleeping)

VP = was dreaming

How do we represent (sleeping) and (dreaming) in the tree diagram, as adverbs or as verbs ?

[Tdol]

They are verbs- present participles and not adverbs.

[Pedroski]

Simplify everything first, you can get more complicated later. You've chosen to look at -ing forms. It can be validly argued that they are nouns, and equally validly argued, that they are verbs. This makes diagramming them hard!
Look up Richard Hudson, Uni. London, who has his own Word Grammar, and does not subscribe to XBar.
Cf We were talking about John having a sabbatical. Think about that for a bit!

Start with the easiest: The boy will dream.

What you label S is called TP nowadays.

[TP [DP [D The] [NP [N boy]] [T FUT will]] [VP [V dream]]

can who sleep?

[TP [DP ] [T PRES can]] [DP [NP [N who]] [VP [Vsleep ]]

[TP [DPi [NP [N who]]] [T PRES can]] [DPi trace [VP [Vsleep ]]

Stick the two together! You can do it! who can sleep will attach at N' right above boy, to make the phrase 'The boy who can sleep' This is a constituent, because you can replace it with 'he' 'He will dream'.

I like these diagrams, but remember: Anthony Kroch (Uni Pennsylvania) said, 'Trees can lie!'
I'm no expert, so don't take this as gospel! But if you want I'll send you my diagrams.