Two suicide letters

Remarkably, in this short time, according to Roazen ,Tausk allegedly wrote two suicide letters, a will, and a detailed list of all his belongings. This doesn't seem possible.
On the other hand, the murderer, assuming Tausk was murdered, could have written in advance the letters, as well as the will, and brought them with him. And ausk may have written the list of his belongings as a preparation for a nuptial agreement.

The bottle of vodka (Slivovitz) on the table (1)

Allegedly, as Roazen claimed, Tausk drank Silvovitz vodka before deciding to take his own life. The claim is to say the least dubiour. It is not believable that Tausk, coming home at that early morning hour, would start drinking, rather than going to bed. After all he knew, he had to get up early in the morning since his bride was coming to meet him.

An alternative explanation

Tausk had a visitor who may have brought the bottle of vodka with him, or Tausk opened a bottle to drink with the visitor.
The visitor must have been waiting outside for Tausk to come home.
He may have approached Tausk on the outside, or knocked on his door.
What kind of visitor would Tausk let in at this early morning hour? Someone with whom he was not only acquainted with but also in some was associated with. Freud was this kind of person.
What happened next? Somehow, Tausk was neutralised, unable to offer resistance. If it was the visitor that brought the vodka, it may have been spiked with some kind of tranquilliser; or Tausk could have been injected with some paralysing drug.
Tausk was a bigger, and at his age of 40, presumably, a much stronger man than Freud, thus, unless he was incapacitated, he wouldn't be easy to overpower. But once it was done, it would have been an easy thing to shoot him in the head, and hang him or vice versa.

The servant sleeping next door not hearing the shot

The claim, that the servant didn't hear the shot because there were soundproof doors and that Tausk held the gun to his temple, is not believable.
A shot from a pistol would have been heard without a doubt in the next room, since it would easily travel through the walls.
One possible explanation is that that night the servant wasn't sleeping in her bed. Or maybe the servant was paid off to be away, or maybe she let the visitor in, and kept quiet about what she did, and heard.

The cross window and the window cross

As it was reported, the servant found her master dead (hanged) at (on) the cross of the cross window. This is a very unusual way of committing a suicide.
Cross window is a rectangular window divided in four parts by a vertical and horizontal bar forming a cross. And, since Tausk was found hanging on the window cross, the two upper windows must have been opened to thread the rope around the vertical bar.
What is surprising is the fact that the cross would have kept up the weight of a man, approximately 75 kg of weight. Things would be different if he was hanged rather than hanging himself. There is also a question how high the window cross was that allowed a man of this height to hang himself. (According to Tausk's son: Physically, he was not exceedingly tall, as has been said. I remember him saying that his height was 1.74 meter.)  (2)

Christian symbolism

Moreover, there's the question of symbolism, and Freud was the master of symbols. The cross is a Catholic symbol, and Tausk had converted to Catholicism when marrying his gentile, first wife, Martha.  (This is how Tausk explained his reason for the conversion: As my fiancée was a Christian and did not want to be converted to Judaism, I myself had to change from Jewish creed to Christianity in order to be able to marry her.) (3)
What also comes to mind is the image of God's son, Jesus, on the cross. Assuming it was Freud that killed him, it is not unreasonable to view Tausk's death on the "cross" as the "son's" punishment for his revolt against Freud, the "father".

(N.B. Nowadays, the house at Alser Strasse 32, where the Tausk allegedly died, had been turned into Hotel-Pension Astra. The windows are no longer cross windows. However, the house number 30, has cross windows as pictured. Possibly, this was the house in which Tausk had died.)
(1)  Roazen, (1969, p. 125).
(2) Tausk, Marius. Marius Tausk: Victor Tausk as Seen by His Son, American Imago, vol. 30, no. 4, 1973, pp. 323–35., p. 323.
(3) Tausk, Marius, (1973, p. 325).

This article presented a different version of the events. Rather than being hanged on the cross window, Tausk supposedly attached a rope to a nail, which is odd. There are no nails in an average room suitable for attaching a rope. Moreover, it is highly unlikely that Tausk would have access to a big nail and a hammer in the middle of the night. And, a nail still wouldn't hold a weight of a man, rather it would've been pulled out from the wall or the ceiling. The whole idea that Tausk hanged himself on a rope attached to a nail is even more bizarre than the alleged fact that he had hanged himself on a cross window.
Notably, Tausk's death was commented upon, allegedly by one of Tausk's friends.
Who could that friend have been, taking into account that most of his comment is a promotion of Freud's own "science" of psychoanalysis? Could the author of the well-informed comment, just as in the Nathan Weiss' case, be the psychoanalytical guru, Sigmund Freud?
There's more than a chance that the whole article was written by Freud, just as in the Nathan Weiss case. A brilliant idea. First you kill someone, then write an article about the deed, and get paid for it.  Without doubt, Freud was goading the  police, and he had a total success dying in his own bed rather than being hanged in his younger years.
Assuming the article was written by Freud, his motivation to publish misleading information about Tausk having hanged himself on a nail is easily understandable. Due to his paranoia, he would have been unwilling to let the readers know that the "suicide" was staged. 

Below follows the comparison of the comments by the anonymous "friend" with the obituary of Tausk by Freud. There's an uncanny similarity between them. Both the article, and the obituary, were published anonymously.

Comparison with the original publications in German

Even if we disregard from other passages, already the last quote from the article - mirroring Freud's obituary of Tausk - reveals Freud as the author of the article published in the Die Zeit (The Time) newspaper the day after Tausk's death. And, there's an interesting question. Why would Freud write the article anonymously? Killing two birds with one stone? Besides getting rid of Tausk, also getting paid for the article? Money for Freud was laughing gas.