Is "Had you eaten before we had arrived?" grammatically incorrect?

It's formally correct, but this sounds like you're talking about the past in the past in the past, which is just confusing and probably not what you meant. If you just meant the past in the past, the second "had" is unnecessary.

In my family, the question was phrased "Did you eat yet?" pronounced "Jeet jet?"

<Did you eat?> ------- < we arrived > ------<other past events> ---- now I talked to my friend and I asked him if he had eaten yesterday before we had arrived at the party But I agree, most people will just say, "did you eat before you got there?" or " Had you eaten before you got there?"

If I’m talking to a friend about whether they’ve eaten before they got to wherever we are, I’m asking like this: “Did you eat yet?” Or “Did you eat before you got here?”

The second ‘had’ is a bit cumbersome, but not incorrect. You’d either contract it to ‘we’d’ or avoid using it altogether. It is correct, all written in the past tense. But what scenario are you trying to use it in? The way it is written is suggesting additional context. This reads to me like someone has eaten _again_ and you are clarifying whether they had already ate. If I was asking someone this question as a precursor to suggesting getting some food, I’d ask ‘have you eaten?’

Correct. Native speakers will say "have you ate already?", but that is because they are bad at following the laws of grammar. 

This sentence is fine It’s talking about two different points that are both in the past. The time the person ate and the time you arrived. In other words “did you eat at some point before our arrival a few hours ago.”

It’s not grammatically wrong, but it’s not idiomatic.

"Had/Have you eaten yet?" is much more common.

Seems a bit clunky but it not incorrect. Second "had" seems unnecessary. I would probably say "did you eat before we arrived?"

"Have you eaten?" Is what most would say.

You're using "had" (Past Perfect) to express that one event happened before another. "Eating" happening BEFORE the "arrival". If you put them both in the same tense, then you defeat the purpose. You put the earlier event in Past Perfect and the later event (both still in the past) in Past Simple. I'm sure the book or teacher had explained this structure to you.

Doesn't sound quite right to me. We usually don't use two "hads" together in such a way. The second clause should just be past tense. "Had you eaten before we arrived?" But in some regions, we would be more likely to hear "Did you eat before we arrived?"

You could read into the intended meaning of this sentence as: "Were you fed *sometime prior* to us arriving at \[such and such place\] *that one time* we went there?" The place would be implied through context. The second "had" is not wrong supposing the person asking is referring to a past event (but not specifying exactly when it happened), rather than if you were sitting next to them in a restaurant and they were referring to having arrived in that restaurant only moments earlier. When you know, or are discussing, the exact moment of time you use simple past tense. The speaker is using past perfect tense for the act of eating, indicating it happened at a previous indefinite moment in time, while using past perfect and participle for the act of arriving, which indicates the eating took place before the arrival and at a previous, but indefinite, moment in time with respect to the eating as well.

It's a bit awkward to use "had" for past yes/no questions. It's better to use "Did". Did you eat before we arrived?

It’s grammatically correct, but the circumstances where you might hear it phrased this way would be very specific. It’s very formal. This sounds like you’re being questioned by a lawyer on a witness stand about the order of events during a criminal trial. In ordinary, everyday colloquial speech most people would say “did you eat before we arrived?”

Pro tip: British speakers use the perfect tenses more than American speakers, while American speakers hardly use them AT ALL

I’d lose the second “had”, so, “Had you eaten before we arrived?”. I will leave the “Why or why not?”. That’s best answered by those who like fitting retrospective grammatical rules to phrases which have just evolved because they sound right to the people saying them.

I would say no. You don't need the second "had." You don't even need the first "had," either. The past perfect by nature already implies that one action happened before another in the past, so using the conjunction "before" with it is redundant. Thus, I would change the sentence to any of the following: 1. Did you eat before we arrived? 2. Had you eaten when we arrived? 3. Had you eaten by the time we arrived?

“Had eaten” (past perfect form) is used correctly here to mean that the action of eating happened before arriving. However, nothing else happens before we arrived, so there is no need to use past perfect again. So instead we use past simple. “Had you eaten before we arrived?”

The second 'had' is unnecessary. Even then, the English is a little formal and stilted for American english, but it might be appropriate in some circumstances. It is the way a nurse or a lawyer might ask the question. It is far more common to ask the question more simply by asking, "Did you eat before we arrived?"

Yes, it's fine. Because you are asking if something HAD happened (in the past) before another event (their arrival, also in the past).