Was sollen Studenten erzielreichen? / Welches Ziel sollen Studenten erreichen?

Your sentence is absolutely correct. My two suggestions are more of an aesthetic advice, rather than corrections. In the frist entence, "erreichen" has a smoother sound to it as the z can sound pretty harsh. "Welches Ziel" is a bit more defined, although not needed.

Ich glaube jeder Mensch ist anders und keine Einzelstrategie würde für alle funktionieren würde.

"keine" with an e, because "Einzelstrategie" is a singular neutral word - there are three different genders for words in German: female, male and neutral (although neutral isn't the right word I think...). Each type has its own endings, articles and such... So attributing words such as "keine" ave to be adjusted to the word.
"Würde" would be placed after the subject. It's correlating with "Einzelstrategie", so it's usually placed right after the subject and before the second verb, which is "fuktionieren" (an infinitiv, a word in its raw state, not correlating with any other word).

Man muss sich vorab überlegen, was man überhaupt erzielreichen möchte.

Again, more of aesthetic advice.

Bei manchen Menschen ist Geld der Schwerpunkt, wobei bei anderen ist Leidenschaft eher vorrangig ist .

Your version is actually how most people talk, words are often misplaced by accident. In this case, "ist" is misplaced. It's correlating with "Leidenschaft" so it should be placed somewhere after. The placement of the other words made it, so "eher vorrangig" needs to be inbetween. Another possible version could look like this: "Leidenschaft ist eher vorrangig bei anderen."

Natürlich ist das Zusammensein von den zweibeiden der beste Fall, aber in der Realität widerstehen die zwei einander oftfunktioniert das nicht immer.

"Beiden" is more of an aesthetic advice, as the numerical version "zwei" sounds less text-like, if you know what I mean.
The ending of the second sentence sounds a bit weird. What I would actually do is simplify it, so that it's easier to read and for you easier to write. That way, we also don't have the repetition of the word "zwei".

Also, wenn Geld das Ziel ist, sollte man den Vorschlag ablehnen.

"soll" is in the present. However, we are talking about a hypothetical scenario, so the verb should be adjusted to this. "Sollte" is the correct form.

Wenn Leidenschaft das Ziel ist, sollte man deihn annehmen.

The same with "sollte".
"Den" is not necessarily wrong. However, we are talking about the offer (Vorschlag) as a third person, so it's best to use "ihn", masculine and singular.

Ich möchte auch kurz mal die Theorie behandelansprechen, die lautet, dass Leidenschaft tatsächlich zum Reichtum führt.

"ansprechen" is again more of an aesthetic advice. "Behandeln" would mean that you'd go in full detail and treat this subject like a patient with utmost care. However, we are talking about something not as serious and for not so long, so I find it best to use "ansprechen" (equal to "talk about").

Gemäß dier Theorie, wenn man etwas mag, investiert er/sie mehr Zeit darein und bemüht sich viel mehr dafür, was folglich zum höheren Geschick in dem Bereich führt, was dann zur höheren Nachfrage für seine Fähigkeiten führt, was letztendlich zum Reichtum führt.

"der Theorie", because we could ask the question "Gemäß wem, welcher, wessen, ..." so we need to adjust the article (see "Genitiv" rules).
"etwas" because "was" is actually the shortened form and should never be used in a formal text. It's not necessarily wrong, but should be avoided.
"darin" without the e (might have also been an accident).

Ich bestreite nicht, dass diese Strategie in zigmehreren Fällen tatsächlich sehr gut klappt.

An aesthetic advice again. "zig" doesn't sound as nice and should not be used in a formal text.

Zum Beispiel: Die Anzahl von Leuten, die sich für Musik interessieren, überwiegt beträchtlich die Nachfrage nach Leuten mit Musikfähigkeiten.

"Leuten" with an n, because it is Dativ. It's a bit hard to explain, but there are also certain words which can indicate the case. "von" is an indicator of Dativ as well as "nach", if I remember correctly. So the subject needs to be adjusted.

Zusammengefasst: Dier Markt lässt sich einfach nicht widerstehen.

"Der Markt" as it is masculine and singular. However, I would actually write the sentence as follows: "Anders ausgedrückt: Der größte Auslöser ist Ruhm und Geld."
Considering you haven't talked about the topic as much, you shouldn't summarize it. The Sentence afterwards is also a bit weird without enough context (Waht do you mean with "Markt" and why is it that we can't resist it?). You didn't explore enough of this topic, so I would reform the whole thing:
"Anders ausgedrückt" = "In other words"
"Der größte Auslöser ist Ruhm und Geld" which is a bit more understandable, because it refers to your sentence "Bei manchen Menschen ist Geld der Schwerpunkt."

Letztendlich schließmöchte ich mit den folgenden Wörter abschließen: Studenten sollten nicht zu irgendetwas ermutigt werden.

"möchte .... abschließen" is an aesthtetic advice. It sounds smoother and less robotic.
"sollten" again a hypothetical situation. Your version is not wrong, but indicates more of a direct tone, something a dictator would say, a rule that cannot be gone against.
"irgendetwas" the same as before, "was" comes from "etwas" and should always be spelled as a whole.

S, sondern sie sollten sie ausreichend informiert werden.

I would actually put a comma there, since "sondern" is an indicator of one. Without it, you could leave it out and make two seperate sentences.
"Sollten" same as above.