Theta Theory

1. I have just finished reading something on the topic (studying on my own), and want to check if my comprehension is correct:

The relationship between an A - position and a Theta position:

1. A syntactic slot can be a theta position iff it is an A position, but not vice versa.

2. An A - position can be assigned null theta role (eg. expletive Subject 'it' / 'there', any other examples btw?)

2. How is it that the 'Grammatical Function' be related to other components of the theory? I mean... It seems to me redundant to talk of the old concept of 'Subject', 'Object' or 'Prepositional Object' here, as a lexical item can c and s - select (given it be a Governor and m - commands the relevant items, of course) other constituents. Why is 'Grammatical Function' incorporated in the older P&P approach? (I haven't come across the Minimalist Programme yet)

3. How can I distinguish between a 'functional phrase' and a 'lexical phrase'? I refer to <an Introduction to Chomsky's UG> by Vivian Cook (1996 ed.) and <Transformational Grammar: A First Course> by Andrew Radford on this, and I don't quite come to understand the distinction between the 2, esp. when Cook says 'Prepositional Phrases are floating between functional categories and lexical categories'. The only more useful way for me to distinguish between the 2 is to see whether a Phrase can be phonologically stressed. I think there ought to be some more... instead. But, je ne sais quoi...

4. I am not sure whether the existence of a D / S structure distinction is devised solely for the purpose of enabling sets of structural descriptions to be explained by UG. This being assumed true, I speculate that this distinction be eliminated in the Minimalist Programme by modifying Merge - Move operation. Is that the case?