phrasal structure

[K Vikram bt cse]

Hi,
	Could anyone please help me out with this.

if we write out a grammar according to the formalisms of HPSG, what will
be the phrasal structure of a sentence like:

John is singing in the bathroom.

(how do we treat the auxiliaries in such a case)

or a sentence like

John saw Mary singing in the bathroom

(in this case isn't there an syntactic ambiguity)

also let me know the treatment of:

Having seen Mary sing John turned on the radio.
The song which Mary sung was melodious.
The song which was sung by Mary was melodious.

Thanks in anticipation.

vikram