I have learned what "home truth" and "home thrust" means. But what is the meaning of "home question"? Thank you very much in advance.
All of these derive from figurative use of the adverb home in such phrases as hit home or strike home, meaning hit the point aimed at.
A weapon which strikes its target (or the person who directs it) is said to hit home. In the same way, a home truth or home thrust or home question is one which successfully ‘targets’ the person addressed and provokes the strong reaction which the speaker ‘aims at’.
Here's an example from a 19th-century sermon addressed to moralists:
I propose this morning, God helping me, to preach a very plain, faithful, and honest sermon; praying that it may come home to some of your hearts. You will find no smoothness about my speech but the very reverse. My sword may have a very mean hilt, but I do trust it shall have a very keen edge, and that it shall cut sharp, piercing to the dividing asunder of the joints and marrow. I shall first of all, put a home question [...] a question to ask of you, which perhaps you may not like, for you good moral people are very fond of your own righteousness. Let me ask you the question, “Is there not with you, even with you, some sin against the Lord your God?”
Anything 'home' means your personal matter/attachment. As you said Home Truth is the bitter truth about yourself pointed out by someone or realized by you. In this sense, Home Question will be a direct question about your personal nature. Nevertheless, it's rarely used these days.
From the OED:
home truth n. a disagreeable fact about oneself, esp. as pointed out by another person.