Conjunction "because" usage?
In spoken language when someone asks: "Why ...?" Your answer can be "Because I want it."
I mean after "because" you add a clause (Subject + verb) and then a full stop "."

But in written language , is it grammatically correct to write: "I can't go. Because I'm busy."?
I mean in written language when can only use because to join sentences, right?

Question

Conjunction "because" usage?
In spoken language when someone asks: "Why ...?" Your answer can be "Because I want it."
I mean after "because" you add a clause (Subject + verb) and then a full stop "."

But in written language , is it grammatically correct to write: "I can't go. Because I'm busy."?
I mean in written language when can only use because to join sentences, right?

Answer

You are correct, in written English "because" needs to be part of a subordinate clause. It can begin a sentence, as long as the main clause is separated from it: "Because I'm busy, I can't go." This word order is not as common as "I can't go,  because I"m busy," though.

Answer

its used in both places 
to answer question and join sentences for explaining  reasons too