Translation:Do you have an older brother?
Chinese always says what kind of relative. Ge ge means older brother Didi means younger brother Mei mei is younger sister Jie jie means older sister Omniglot has a chart https://www.omniglot.com/language/kinship/chinese.htm
The singular is correct (see the answer at the top of the page). Your answer was wrong because the singular has to be "do you have AN older brother?". You cannot leave out the indefinite article for the singular, but you can for the plural "do you have older brothers?" If your answer is wrong Duo tries to give a correct version that is close to your answer, so it came up with "do you have older brothers?" I cannot help with the Chinese, but I assume that if Duo suggested the plural form then they are both correct.
Duolingo translates "Do you have an older brother?" into "你有哥哥吗?"
Without a measure word "哥哥" can be singular or plural. It refers to brother or brothers, but Dulingo only accepts the singular right now.
"吗" is always used for yes/no-questions.
A better translation of "Do you have an older brother?" is 你有一个哥哥吗? In this case 一个 is "a". Now the question asks for one brother only!
你有哥哥吗? would generelly be translated as "Do you have any brothers?"
Another way to ask "Do you have a brother?" is 你有没有哥哥? Instead of adding the question marker 吗 the verb of the question is used in its yes/no-form 有没有.
Both 吗 and 有没有 ask for yes/no answers.
Dialog example: Person A: 你有哥哥吗? Person B: 有，我有一个哥哥。
The verb is used as the affirmative and it is specified how many brothers Person B has.
At the moment (Family 1, lesson 2) all we're taught is that gege is 'brother' not older not younger.
There was no 'a' and the answer wanted 'brothers' but there was no option for this either. So I just answered with brother and this was accepted. Not the best solution in the world but still!