Specifically, this is father's younger brother.
Technically speaking, yes. But it's also a generic form of address for an older male relative.
"Today's my uncle's birthday" should be accepted too
I wrote this too
I wrote this too!
my uncle's birthday is today should be accepted
"Today is the birthday of my uncle" should also be accepted.
I think Duo, in any course, prefers standard translations. Though "today is the birthday of my uncle" is a literal translation of the sentence, it is awkward and unnatural.
Is 叔叔 an acceptable way to talk about your mother's brothers? And if not, can we assume some people love their mom's family, not only their dad's? 舅舅, Duolingo. Did the 5 seconds of 'extra' work for you. Now can you please pretend mothers matter?
叔父 I think this more adequate.