We would never say this in English; we would say, "Anna's apple is red".

This sentence seems to have two correct answers: "Mărul Anei este roșu" and "Mărul lui Anna este roșu".

Is there any difference between them? As far as I know, whenever a noun or a personal name ends in -a, it must change to -ei rather than follow the "lui [Nominative]" form.