Hi, Dawn -- I'm not sure the implication of "expertise" is carried in the grammar. Using "the" creates a definite reference (hence the name, definite article) to a specific thing. Expertise, you are right, clearly develops from "reading the research," that is, reading research previously mentioned or known to the reader. Expertise is implied more by the sentence's content and meaning and less from its grammar, methinks.
Agree with everything you said, here.
A lot depends on situations. For example (and this is testable) I'd expect more people to ask "what research?" if you leave out the "the".
In sentence A, see if you might agree "in" is best described as a preposition. And, as written, the prepositional phrase "in my garden" might easily describe the position of either the subject (my cat) or the position of the object (birds). It's ambiguous.
Again, I agree. Actually, I'd say that "in my garden" is a prepositional phrase in both sentences, but that it's an adverbial phrase (defined through sentence function rather than word type of the head) in A, and an adjectival phrase in B; or that it modifies the verb in A, and that it modifies the noun in B (terminology I'd prefer, actually, so I shouldn't have said "adverbial", heh).
As to the ambiguity, you're right again, except that - sorry for being nit-picky - it's not the position of the cat, but the position of the action of hunting. If you want the position of the cat your only option is, "The cat in my garden is hunting the birds," as the modifier ought to be part of the noun-phrase. There may be exceptions I can't think of right now, of course.
In sentence B, "in" remains a preposition. Adding a definite article to the object makes it "definite" which birds your cat hunts. Your mean old tom is hunting the birds in your garden (and not hunting the birds on your roof).
Actually, if "the birds" refers to previously defined birds, "in my garden" could still be read as modifying "hunting"....
That's why context is always important, I suppose.
You are absolutely right: even very small changes in grammar can create large alterations in meaning. Adding a little old "the" can spell the difference between a cat who's in the garden and a bird that isn't, anymore. Cheep! Cheep! Che..!
And the amazing thing is that most people get it right until they start thinking about grammar. But perhaps that isn't so amazing after all.