The eleventh is not about Daniel himself, but something female, that is the eleventh Daniel has.
Again, this should be "Daniel o are pe a unsprezecea." = "Daniel has the eleventh one." The way it is written currently it needs a noun: "Daniel are a unsprezecea carte." This is an issue throughout this unit.
The correct sentence with 'o' has also come up in this same lesson for me. I had to translate from English to Romanian. As it was the first time I had seen the sentence, i omitted 'o' and was told (rightly) that it was incorrect. However now doing it the other way around, Duolingo seems to indicate that 'o' is not needed. I think thid sentence needs reporting
Because Daniel has a feminine object, indicated by the feminine ordinal number. Gender in romance languages is usually determined by the possessed object, rather than the posssessor. Italian is the same.