I would say [name_u]Audie[/name_u] over [name_f]Aud[/name_f]. I adore [name_u]Audie[/name_u] (like npr’s [name_u]Audie[/name_u] Cornish) personally, but it is definitely avoidable.
of course not, how silly. this is like asking if the name [name_u]Noah[/name_u] would be shorted to No.
[name_f]Audrey[/name_f] is a popular name has no need for a nickname, many, many names don’t and therefore never get one.