"Die Hälfte hast du."
Translation:You have the half.
because du is nominative, making "you" the subject.
edit: also, "part" is "teil," not "hälfte."
Probably not normally; usually the "object" (which receives the action of the subject's verb) will be at the end. Just be aware of cases in German. "Der Hund beisst den Mann" and "Den Mann beisst der Hund" are equivalent. The first is more common, but the second stil makes sense due to cases.
While Duolingo loves to do this and, as casezer wrote, it's grammatically perfectly alright, you would be safer to put the subject at the beginning of the sentence. It's used more often that way, unless you wish to particularly emphasise a different part of the sentence.