Bdtyk

Observation

Take a subject that contains an of-phrase (friend of X, president of X, writer of X etc.). Now try to question the element X after of by fronting the corresponding wh-phrase.

Often this seems to be completely impossible, as illustrated in (1).

(1) [The friend of the president] has arrived / was fired / fixed my car.

--> ?* Which president has [the friend of _ ] arrived?

--> ?* Which president was [the friend of _ ] fired?

--> ?* Which president did [the friend of _ ] fix my car?

But sometimes such fronting seems to be fine, as shown in (2).

(2) [The impeachment of the president] has occurred / was discussed / caused outrage.

--> Which president has [the impeachment of _ ] occured?

--> Which president was [the impeachment of _ ] discussed?

--> Which president did [the impeachment of _ ] cause outrage?

And sometimes, such sentences are more acceptable for unaccusatives (arrive, occur, die) and passives (was fired, was discussed, was arrested), than for transitives (fix my car, cause outrage, composed a speech). This is illustrated in (3).

(3) [The writer of the president] has died / was arrested / composed a speech.

--> Which president has [the writer of _ ] died?

--> Which president was [the writer of _ ] arrested?

--> ?* Which president did [the writer of _ ] compose a speech?

Question

Why can you sometimes leave of stranded in the subject and sometimes not?

You are attempting to follow a pattern in informal, unscripted spoken English in which an interrogative is fronted, stranding the preposition:

Interrogatives with preposition fronting are heard in prepared and organised speech, as in a planned interview (To what do you attribute this trend?), but in ordinary conversation the stranding construction is strongly preferred. — Rodney Huddleston, Geoffrey Pullum, A Student’s Introduction to English Grammar, 2005, 138.

Preposition fronting also occurs in tests and quiz shows (Of what country was Maria Therea empress?) where topicality and clarity dictate the word order. All of your examples, most would agree, would sound far more idiomatic had you fronted the preposition rather than the interrogative.

There is ample attestation, however, for the preference for preposition stranding:

So I was talking to the President about appointing him. He said to me, ― Who’s he a friend of? ‖ I said, ―Well, he’s a friend of Ed Day’s. — Richard K. Donahue, recorded interview by John F. Stewart, March 8, 1967, (17), John F. Kennedy Library Oral History Program.

Well, we may ask, then, who’s he a friend of? I'll tell you who he‘s a friend of. He’s a friend of big business and of the rich of this nation. — AFL-CIO Free Trade Union News 35–39 (1980), 13.

“Who's she a friend of?” “Mary Nichols.” “I've never heard of her.” “Old friend of mine. Honestly, Babs, you'll like this girl.” “Well, ask her to dinner.” — Evelyn Waugh, The world of Evelyn Waugh, 1958, 176.

Q: The keeper of the woods is Jim Green. Who is he the father of? A: Lilly Ingram. — Greenvale Trivia

Who is she the mother of, again? Every possible answer seems utterly wrong. — The Bible (Annotated): Genesis 3.

Who is she the sister of?— Headline, IMDb

What country is he the president of anyway? — Daily News (Los Angeles) 3 Feb. 2006.

Except for an adverb (again, anyway), the preposition of is truly stranded — at the end of the question. You are attempting to use the construction within a noun phrase where the preposition establishes a genitive relationship between two nouns (x of y), which requires a reparsing of the sentence once the hearer/reader encounters the preposition.

Huddleston-Pullum adduces the following sentence (139), which it terms “fairly clearly ungrammatical” because it occurs within a subject noun phrase:

This is the safe which the key to was stolen.

I would suggest that your examples suffer, though interrogatives, from the same problem.