Is this the actual "comparative" form of the Russian "younger" or does it just have the same general meaning as a "younger brother" / "little brother"?
It's an interesting question amaybury because from what I understood this is in fact a special case of (long form) comparative where the comparative is constructed without более (more) or менее (less). Other adjectives that have of long form comparative of their own are: больший (bigger), меньший (lesser, smaller), лучший (better) and худший (worse),... and старший (older) and младший (younger) (the latter two only when they refer to animate nouns or groups).
Enter a word here to see all the forms: http://starling.rinet.ru/cgi-bin/morphque.cgi?flags=endnnnnp
Alternatively, search for it on Wiktionary and expand Declension: https://en.wiktionary.org/wiki/%D0%BC%D0%BB%D0%B0%D0%B4%D1%88%D0%B8%D0%B9
Hmm, yes, but grammatically correct is not always the same as everyday language, which is what Duolingo seeks to teach. I would correct my 11 year old French pupils if I saw this in a piece of homework, because it is the sort of difference that would mark them as foreign. 'Have you got' or 'do you have' would be more natural to (most) native speakers and ears.
It's because of the peculiar construction used in Russian for 'have'. Basically, in any sentence with 'у [тебя/меня/etc.] есть, the item you have will be nominative.
I think of it as translating literally to: 'of me there is a brother' or 'there is a brother of me'. Then it makes sense gramatically because it's always nominative when you say 'there is a thing'.