Well, here's my assumption of those questions. These are from my own standpoint and if anyone else out there reading this has their own opinions or their own awnsers, feel free to post as well.
How did they identify Mickey Scellenda?
My best guess is when after Jane was murdered in the hotel lobby that when the police investigated, they may have found out Scallenda's name either from the hotel registration form, or from witnesses (such as the front desk clerk) who may have given them a discription of Scallenda.
How did Fay realise the killer didn't have two fingers? After all, the real killer did. Did she imagine Mickey to be the killer?
That's mostly left up to interpertation that Fay was described to be somewhat psychic, that she thought Mickey Scallenca was the killer when he attacked her on the subway train, but when the real killer attacked her, she may have had a dream or vision about the real killer.
How did they identify that the killer was from new york?
There is no way to comfirm that from one's blood type. An absurd plot loophole.
How did they determine the killer's age?
Again, no possible way to make out a person's age from their blood type from back then to today.
How did the killer find out about the secret hideaway of the inspector?
Again, another farfetched plot twist that is never explained and left up to the viewers to decide. It may be possible the ripper could have looked up William's past records, or followed him to Kitty's house, but that is never fully explained in the movie.
How was Mickey so stupid? what did he intend to get away with when he attacked Fay right inside her house?
He probally thought that Fay would identify him as the New York Ripper since he attacked her on the subway train. He broke into her house to apparently kill her in order to prevent her from talking more to the police.
Was the real killer following Mickey Scellenda around? They seemed to be at the same places.
Apparently, yes. As Professor Davis explains in one scene that the killer used Mickey Scallenda to randomly pick out his victims from porno houses to the Staten Island ferry by having Mickey tail them and leave them for the ripper to kill. The phone call that Mickey made in the hotel room, where Jane was tied up, was apparently to the killer explaining where he was and about her which explains how the killer arrived later to kill her as she was leaving the room. But how and when and why did the killer recruite Mickey to be his patsy and scout for victims is another baffling twist not explained in the movie.
What in Fay and Peter's story did the psychologist become suspicious of?
From Peter's behavior over Fay's attack at how he knew where and when she was and apparently other details that only her attacker would know.
Who called Peter/Fay in a duck's voice towards the end?
It was his daughter Suzy from her hospital bed. She called Peter, her father, to talk to him playacting as 'the Little Duck' whom she was inspiring him to kill women, while Fay was listening in on anther line which made her realize that her boyfriend was the killer this whole time.
1. What is Dr. Davis' rationale behind the killer being highly educated and refined and intelligent? It doesn't take a smart man to be able to do a donald duck impression LOL.