"The sisters are drinking tea" would be "Die Schwestern trinken Tee". There is nothing in the German sentence that indicate that they are only sisters, so if you translate it with sisters you are restricting the meaning of the sentence. If it would have been known that there were only sisters, then "Schwestern" would have been used. It is similar as when you have a sentence about a child ("Kind") and then translate that with "boy" (or alternatively "girl"). Nothing warrants that translation.
I think it is perfectly correct to translate "Geschwister" as brothers and sisters. Actually when one hovers the mouse over the German word the translation is exactly that. Siblings is a rather "psychology word". It is a more usual thing to say brothers and sisters. I should not have been marked wrong for this.
Is Geschwister always plural?
In practice, yes.
Does Geschwistern mean anything?
Yes. It's the dative plural form (with the -n that's typical for dative plural forms).
Is there a word for sibling, not siblings?
Not a very commonly-used one. Bruder oder Schwester might be used.
I've also seen Geschwisterkind, but only in the context of school admissions.