***** NOT A TEACHER *****
(1) First, good luck on your test. I KNOW that you WILL do very WELL on it.
(2) You are much smarter than I. I never could understand big words like "deontic."
(3) No. 1. The Oxford Dictionary of English Grammar defines "prepositional complement" as:
The word or phrase "governed" by a preposition . (Also called object of preposition.)
in the end
before the war
afraid of being killed
So I guess the answer to No. 1 is YES!!! (I didn't know that until I read it this morning. Thanks for teaching me something new.)
I do not have the confidence to touch No. 2.
No. 3. I agree with your teacher.
If you remove the clause, you get "The claim is unfounded."
Of course, someone would ask "What claim?"
Then you would say:
Oh, that they found a cure.
I believe books say that "that they found a cure" is a noun clause in
apposition with "claim." (It explains "claim.") As you know, you could
delete (erase/drop) "that."
You ask whether a predicate nominative is the same as a noun clause.
Well, I think the answer is NO, BUT a noun clause CAN be a predicate
nominative. Here is an example from my favorite grammar book
(Descriptive English Grammar by Professors House and Harman, written
in the "olden" days of 1931):
The question is whether he can be nominated.
(The noun clause "Whether he can be nominated" refers to "question.")
Of course, I would not even dare to try answering No. 4.