Janice a-t-elle écrit la lettre ?

A Janice écrit la lettre ? is incorrect ; subject and verb are inverted only if the subject is a pronoun. In other cases, the construction is [subject][verb]-[pronoun].

Janice, a-t-elle écrit la lettre ? is a bit weird : this comma doesn’t make much sense.

Janice, l’a-t-elle écrite ? (the past participle agrees with the object if the object is before the participle ; here the object is l'[a lettre] ad comes before écrite) is not something we would say or write. Topicalization (separating a subject from the rest of the sentence and repeating it with a pronoun : [Janice][…][elle]) is something you’d find in oral or colloquial French ; subject – verb inversion is more often found in written language, so this construction is a bit awkward.