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I might have a question: Would you be willing to answer a question? I wonder if you might possibly be willing to consider a question? And so on. Some might consider "I had a question:" a gentler and more polite expression than "I have a question:" because it implies that the question hasn't been constantly on your mind; it arose once and is ...
tense - "I had a question" or "I have a question" - English Language ...
It is common to say or be asked "Any questions?" or "Do you have any questions?" Using got doesn't work at all for me: only in the context of asking a speaker "Did you get any questions?" So if I got a question, it would be asked of me not by me.
word choice - Got questions? VS Have questions? - English Language ...
The most common form of the question, in both British and American dialects is "Do you have..." Using "Have you" is a non-typical use. It sounds old fashioned. For example there is a nursery rhyme which goes: Baa baa black sheep, Have you any wool? There is a similar form "Have you got a map". This is quite common in some British dialects, but is frowned on by some teachers.
When properly quoted for Google search, the numbers are: "I have a question for you" 28M results, "I have a question to you" 3M results. If usage on the net is a guide, the former over the latter 10:1.