Learn English – Using “had” vs “have” in conjunction with “previous”

I have a question.

Present tense. Right now I have a question.

I have had a question

Perfect tense. At one point, I had a question. It may or may not be true that I still have it now (might be made clear from the rest of the sentence).

I had had a question.

Pluperfect. At one point it was true that at an earlier point it was true, that I had a question. "I had had a question for some time, but I never got a chance to ask it".

Now, in each of these the verb have is used once in the sense of "to possess" or "to hold" and in each of the second two it is used as an auxiliary to modify that other have.

You propose.

?I have had had a question.

Which we would presumably have to interpret as some sort of super-perfect stating that at some point it was true that at an earlier point it was true that at an earlier point it was true, that you had a question. It's not clear what you are saying about the current state.

As such, you've just created a non-standard variant of either the perfect or the pluperfect, but you leave us confused as to which - and imply that you are confused about the matter yourself.

You suggest it might be better as:

?Having had had a question, I asked it.

But this presumably would mean that it being true that at one point it was true that at one point you had a question. Again, it's not clear just what this is supposed to mean, and one possible interpretation has this as impossible (because one way of untying the knots leaves us with the suggestion that you no longer had a question at the time you said it).

In all, this reminds me of some comic nonsense writing that has been done - sometimes well - but were the whole point of it is that it was not good English. Barring that goal, none of this makes any sense.

You talk about "unique time travel situations", and I could see someone deliberately engaging in this sort of abuse of auxiliaries to describe that. Still, the implication is "this time travel has so messed with the logic of causality that English grammar can no longer work to express the resultant mess". Once you're doing that then you've deliberately thrown the rules of grammar away for effect anyway, so asking if it's grammatical is not just besides the point, but counter to it.

Really though, this is not grammatical English. Nor is it a useful construct to anyone who perceives time and causality as being related things.

The Oxford Dictionary Online (a proper noun) defines proper noun as

A name used for an individual person, place, or organization, spelled with initial capital letters, e.g., Larry, Mexico, and Boston Red Sox. Often contrasted with common noun.

[It also conflates proper nouns with proper names, and I will not try to sort that our in this answer.]

As the questioner suggests, Wikipedia defines it as

a noun that in its primary application refers to a unique entity, such as London, Jupiter, Sarah, or Microsoft, as distinguished from a common noun, which usually refers to a class of entities (city, planet, person, corporation), or non-unique instances of a certain class (a city, another planet, these persons, our corporation).

I disagree with the criterion of unique. Rather, a proper noun refers to a specific instance of something. During the bestowing of a proper noun, the naming entity seeks to distinguish the individual accorded the proper noun from others in the generic class. When my father named me Dopey, he sought to distinguish me from my brothers, Bashful and Doc, and whoever else might come along later. He didn't especially care that Mrs. McGillicutty, three streets over, had also named her son Dopey. Within our circle, Dopey meant me.

There are very few proper nouns that are truly unique. The number of towns named Springfield, Madison, and Franklin are in the dozens apiece. However jurisdictions resist identical names within their purview. A town near me was named Marion and was called that for decades before someone in the state realized there was another town of the same name and our neighbor was rechristened East Marion.

If it were just me and Dad on a desert island, naming me Boy might work just fine. And maybe if only I were in the room and he said Now listen to me, Son, that would be okay. But when he yelled up the stairs, son, all his kids responded or no one did.

To each of us, Dad means the specific Dad (or sometimes Dads) that relate most closely to us. I had a mother and a stepmother, both of whom I called Mom. I can speak of my two moms, but when I address them or use them without a limiter (such as my mom), I refer to them in the capital.

To sum up, things that are virtually never grouped into a class and have been named to be specific within their own circle are always captialized, even when they are artificially aggregated.

• All the Alberts in the class should stand.
• There are many Washingtons in the US.

These retain their upper case status even when they are converted to a category with a modifier

• The Microsofts of the world will have to rethink their strategies.
• The Roosevelts were a political and social force to be reckoned with.

But common nouns that are used as a term of address or in lieu of a name without modifier are capitalized in those circumstances, but lower case in others. So

• I asked my mother to come over.
• I asked Mother to come over.