Translation:One of the girls is short, the other one is tall.
I said "and the other is tall" because on a different sentence I was counted wrong for not including "and" even though the construction of the sentence was the same.....a comma followed by "a másik". This time I was counted wrong for including "and". It seems inconsistent. Neither time used "és".
By my opinion your translation is not correct, since "One of the girls is short, the other one is tall." means "Az egyike a lányoknak alacsony, a másik magas.". "Az egyik lány alacsony, a másik magas." should be translated to "The one girl is short, the other one is tall.". Your translation uses girls (plural), and missing the definitive article (az).
Does this construction of 'egyik ..., a másik ...' imply, that I am referring to a group of two objects?
And furthermore, does the usage of just 'egyik ...' imply the same thing, or does this rather apply more generally to greater groups of which one object/ person etc. is picked?
Yes, 'egyik ..., a másik ...' implies a group of two.
Just "egyik" : it can be a group of any size.
"Az egyik lány alacsony" It can be that in a group of ten girls, one of them is short.
You could say: "Az egyik lány alacsony, a többi pedig magas." In the group (any size) one of the girls is short, and all the others are tall.
(But do not use egyik ... többi if there are exactly two people, in that case, switch back to egyik... másik )