Please read these examples first and read my long answer given below.
6번 출구는 어디로 가야 하나요? (✘)
This is an incorrect sentence because it has to be the same as either "6번 출구는 제가 어디로 가야 하나요?" or "6번 출구는 우리가 어디로 가야 하나요?". This 6번 출구 is kind of isolated from any other word in the sentence. The implicit/omitted subject of 가다 must be a person ("I" or "we") not the exit. You cannot say "6번 출구가 어디로 가야 하나요?", either, because it is not that the exit should go somewhere. You should say
6번 출구는 어디로 가야 나와요?
6번 출구는 어디로 가야 있어요?
For these two sentences, you can also use the subject marker 가 (preferably with changing the word order):
어디로 가야 6번 출구가 나와요?
어디로 가야 6번 출구가 있어요?
Why should you change the word order? The reason is simple: The implicit subject (저 or 우리) is connected to 가다 and another subject, 6번 출구, is connected to 나오다 and 있다. The relativeness between words determines the most natural word order in a sentence, although it is not an absolute rule.
6번 출구가 어디인가요?
You can also say
6번 출구는 어디인가요?
but the context will sometimes make you choose one. In the case when your interlocutor told (or is telling) you where other exits are but you wish to know where Exit 6 is, you need to use the latter one, since you are changing the topic. The same logic goes for other sentences:
6번 출구가 어디예요?
6번 출구는 어디예요?
6번 출구가 어디죠?
6번 출구는 어디죠?
Now, you should keep in mind that 어디에요 is a misspelling. Such a mistake is common because for convenience, a lot of people pronounce 예요 as 에요.
You can use this question only when you have heard the locations of other exits. On the other hand, when you use the sentence
you have the intention of confirming what you have heard about the subject Exit 6. For example, when you heard
6번 출구가 저기에 있대.
you can say "6번 출구가요?" then.
(네가 가장) 좋아하는 과일이 뭐야?
This sentence means: "What is the fruit that you like most?" Roughly speaking, 는 of 좋아하는 functions as "that" or "which". This 는 is not a marker that you mentioned but an ending for verbs. 좋아하다 is connected to the (clause) subject 너. 과일 is the (main) subject here.
이 of 과일이 is one of the subject markers. Here, you can use 은 (one of the topic markers) instead.
망고는 제가 가장 좋아하는 과일이에요.
This sounds too awkward because the topic was about "the fruit" not about "mango." No native Koreans will answer the question in this way.
제가 가장 좋아하는 과일은 망고예요.
This sounds much better. The topic is "my favorite fruit." If you use the sentence
저는 (제가) 가장 좋아하는 과일이 망고예요.
instead, it implies either that you wish to know what fruit others like most or that it is your preference not others' because 은/는 are also the markers for implicit or explicit comparison.
저는 망고를 제일 좋아해요.
This is one of the best answers. You are talking about yourself (your favorite fruit), so the topic can be "I" (저). How about the following sentence that uses a subject marker instead?
제가 망고를 제일 좋아해요.
This shows that the one who likes mango most is "I", which means that "I" do not think others like it as much as "I" do. As a side note, there is a sentence translated as "I am the best!":
내가 제일 잘나가!
It implies not you (or not others) but I am the one. In this context, you cannot say
나는 제일 잘나가! (✘)
... you should use this sentence structure when comparing qualities of the same person/thing: A는 ~인데 B이/가 ~하다.
I wonder who told you this. 은/는 can be used in place of 이/가 there.
이 카메라는 품질은 좋은데 가격이 너무 비싸요. (✔)
이 카메라는 품질은 좋은데 가격은 너무 비싸요. (✔)
Using 은/는 is usually better because of the following exception:
나는 춤은 잘 추지만 노래가 잘 못 불러. (✘)
나는 춤은 잘 추지만 노래는 잘 못 불러. (✔)
나 is the topic (and also the subject here). 은 of 춤은 and 는 of 노래는 are used to compare two abilities (춤 and 노래) that the topic has. I mean these 은 and 는 are the markers for comparison. Why is 노래가 incorrect? 노래 is the object (not the subject) connected to 부르다; 나 is the subject connected to both 추다 and 부르다. The following sentences are also correct:
나는 춤은 잘 추지만 노래를 잘 못 불러. (✔)
나는 춤을 잘 추지만 노래를 잘 못 불러. (✔)
By now, you should have noticed that the target marked by 은 or 는 is various: the subject, the object, ....
Details on "6번 출구는 어디로 가야 하나요?"
"6번 출구는 어디로 가야 하나요?" is semantically the same as "6번 출구는 제가 어디로 가야 하나요?" or "6번 출구는 우리가 어디로 가야 하나요?". It seems that your friends misread my explanation. The point is not about whether you can omit the subject but about whether the sentence is logically perfect. An incorrect sentence equals another incorrect sentence, which is what I meant with "... it has to be the same as ...".
6번 출구 is a noun phrase. A noun phrase can be used with or without a marker in a sentence as one of components including a subject, object, complement, adnominal phrase, adverbial pharse, and exclamation (When attached to 은/는, it is used mostly as a subject or object). Using 는 in place of another marker right after a noun phrase does not change which component the phrase is.
가야 하다 requires two components: (1) the subject, and (2) either the adverbial or object referring to the destination or direction. The subject is usually marked by 이/가 (although it can be omitted in some cases); the adverbial used with 가다 usually has one of these markers: 에, 에게, 한테, 께, 으로, and 로; the object markers are 을/를. Thus, the general structure of sentences using 가야 하다 is "...이/가 ...에/에게/한테/께/으로/로/을/를 가야 하다." In that sentence, either 저 or 우리 is the subject and 어디 is the destination or direction because you are asking where to go. Therefore, the sentence does not need 6번 출구, which means that the sentence is incorrect. I said 6번 출구 is "kind of isolated" because 6번 출구 is not required by the other words in the same sentence:
In that sentence, can 6번 출구 be a
subject? No, no verbs are using 6번 출구.
object? No, no verbs are using 6번 출구.
complement? No, 되다 and 아니다 are all absent.
adnominal phrase? No, an adnominal phrase cannot have 는 right after it.
adverbial pharse? No, no verbs are using 6번 출구 and 6번 출구 is not a sentence adverb.
exclamation? No, it cannot be there.
From this diagram (generated via this site), you can see that 6번 출구 conflicts with the subject (I used red underlines) and also with the adverbial (I used green underlines):
Now, do you understand why I said that "6번 출구는 어디로 가야 하나요?" is incorrect?
Do your friends think it is correct? Then, it may be because they are familiar with sentences such as "저는 어디로 가야 하나요?" ("Where should I go?") which is correct because it has the "human" subject 저 attached to the marker 는. In this case, "저는 제가 어디로 가야 하나요?" is incorrect because the subject is already specified. They may notice the incorrectness of "6번 출구는 어디로 가야 하나요?" when just replacing 저 in "저는 어디로 가야 하나요?" with 6번 출구. You are not saying "Where should Exit 6 go?", are you?
You said you are getting conflicting information from native Koreans. What is important is that none of us is perfect. Unfortunately, most Koreans are not excellent at (the prescriptive) grammar. In addition, it is quite difficult to consider everything in an actual conversation. I do not think I am an expert, but I believe I think more logically than my friends.