Learn English – Usage of your and yours

The correct phrasing is my question is.

As you rightly note, my is a possessive adjective and mine is a possessive pronoun. So, this means you use my where you already have a noun (such as question) and want to indicate ownership. Like with all pronouns, you use mine in place of another noun when it's understood what's being discussed.

Mine question is is ungrammatical, because it incorrectly uses two nouns (mine and question) as the subject of a sentence. You use either a noun or a pronoun, never both at the same time. Use a noun (my question) if the topic is just being introduced, or a pronoun (mine) if the reader or listener will already know you are talking about (they will know you are talking about your question).

The following are correct:

• My question is [something] uses my to indicate whose question is being described.
• That question is mine uses mine to refer back to the subject (that question) and add information describing whose it is.
• Mine is [something] describes some object of yours (e.g. your question) which was previously named and is currently the topic of conversation.

I think that this is confusing because you're using your and my when we already have a word our which would normally be preferred. For this reason the sentence is a little awkward, because it's not really clear why the writer has decided to not use our here.

If you want to use your and my for emphasis, which you certainly could do, then it would be a good idea to use the marker both here to highlight this:

Both your and my grandparents grew up listening to this piece of music.

This sounds perfectly natural and correct.

With regards to yours and mine, this is ungrammatical. The reason for this is that in modern English we never use mine or yours when there is a following noun.

• It's my elephant.
• It's mine.
• *It's mine elephant. (ungrammatical in modern English)

I think your last sentence is a bit awkward because there doesn't seem to be any benefit in terms of meaning or effect for using such a complex construction when our grandparents would seem to do the same job.