Differences of yes and no.

ain't = is not, are not, am not (have not , has not etc.).
aren't = are not.
gotta = got to.

The use of "yes" and "no" does not depend on the use of positive and negative verbs, but on positive and negative answers.

Example 1:
Question 1: Are you hungry ?
Question 2: Aren't you hungry?
Answer 1 to both questions: Yes, I am hungry.
Answer 2 to both questions: No, I am not hungry.

Example 2:
Questions:
Will you join us ?
Won't you join us ?
Answers to both questions:
Yes, I will join you.
No, I won;t join you.

If you are a boy,how would you answer the question?
Yes, I am.

and what's words like ain't ,aren't and gotta mean?
"ain't are't " are both contraction which mean "am not""are not" respectively.
"gotta" is a short form of "get to".

depends on the positive and negative verbs?
No matter the question asks with positive or negative,
You must awnser like:
Yes, I am a boy. or
No , I am not a boy