To sort of start with your tangential question. The reason for the move from exile and execution started under Lenin but really gained headway during Stalin. The idea behind the GULAG system was instead of imprisonment or exile was, in a twisted way, a system of rehabilitation. Work for ones country was both your penance and also to teach you to work and not be a drain of society, in theory. There was also the fact that many of the upper echelons of the Soviet government were former revolutionaries who had been exiled... and somehow always returned, may have swayed the idea against exile. There can also be an argument that the GULAG system itself was an economic system, to force people to complete unpalatable goals; the digging of a canal, building in the frontier.

Now lets start in on the meat of your question.

How were people tortured?

So we do not have any exact "methods" of interrogation from the Soviet Union that I know of. Instead we have primary sources from prisoners. Alexander Solzhenitsyn detailed the methods of Interrogation in his book The Gulag Archipelago. He wrote of ways the NKVD interrogated himself and other prisoners he interviewed.

The main ways is not physical; there was no medieval racks or iron maidens. Instead it was more psychological torture or even physical, but not direct beatings.

• Sleep deprivation was inevitable
• Use of light, either blinding or lack of any light.
• Cold or extreme heat.
• Isolation from everything.
• Starvation
• Forced standing for days at a time was seen quite a bit.

Most of these would be used in combination along with other techniques but it really depended on the time period as well as the criminal and the officer in charge. For a more in depth version there is an abridged version of the chapter from A. Solzhenitsyn found here.

Who performed the torturing?

The arresting officer was in charge of proving "guilt." The easiest way was through confession. There was no need for physical evidence and in the eyes of the court, admission of guilt was the strongest "proof."

Did the NKVD just want confessions, or denouncement of names?

The NKVD officer wanted to prove he was valuable. Value was based upon arresting of crimes, either really committed or not. In a CIA document about Soviet tactics they make special note on this with the following:

"To a certain extent, officers are judged by the number of arrests which they obtain. Since communist legal principles demand no person be arrested except when it is clear that he is a criminal, officers who arrest men who must be released are subject to censure. They have made a mistake because they have arrested a man who is not a criminal. The consequences are important from the point of view of the victim. In effect, any man who is arrested is automatically in the position of being guilty.”

Alexander Solzhenitsyn reiterates that by basically saying, if you have been brought in to the NKVD, you are already guilty... you just may not know it yet.

The other examples were the high profile cases. These were treated differently, because in essence they wanted to prove a conspiracy, such as the "Leftist-Trotsky plot." These they wanted to create a web of confessions that all tied together. So having implicated others you may meet some leniency, although most were ultimately shot.

Did everyone tortured break?

Ultimately, I believe most did break. The question was more the extent of the interrogation, or rather how long they held out for. There is one unique example; Bukharin. He signed a confession of guilt, but edited it so that it wasn't palatable to Stalin. The court forced his testimony where he was to plead guilt, but in a way he exonerated himself in double meanings and sarcasm. Ultimately the court session was simply not publicized, even though ironically foreign press was there at the court, they simply did not understand Bukharin's resistance.