Yes, unfortunately. The governments of the following countries, among others, rely on polygraphy to varying extents: Canada, UK, Israel, Russia, Ukraine, and China.
No, they would just break your fingers or <insert torture> until you admitted to basically anything just to make them stop. They didin't need a polygraph for that, just a hammer, a drawer or a door.
The Panetta review (CIA-internal) and the SSCI torture report (one of those "S"'s are for United States Senate) concluded that torture is largely inefficient at extracting information from extremists. You can torture someone for years on end with them still keeping the things you ask from you. Someone who doesn't know anything, will tell you anything, while someone with deep faith will feed you shit.
It's true, however that didn't matter much in the USSR. What mattered is that somebody got punished, paperwork was taken care of and the agents were doing their jobs. All of this is nicely illustrated in the Citizen X movie, although in a different context.
Citizen X is an American drama. If it depicts what you're saying (I've seen it but can't remember it) then it's just another Western dramatization depicting post-Stalin Soviet Union in cliches from the 1930s.
In the real life case Citizen X is inspired by[0], nobody was tortured for a conviction, even the guilty man, who was simply put into a cell with a police informer to gather information and questioned normally by investigators who only had ten days under Soviet law to release or charge him.
> How do you think the wrongly arrested people confessed to the murders in the first place?
As in that example with Kravchenko, the same way false confessions occur in every country, pressure in some form from the police who want to convict their prime suspect / clear up a case.
It's indefensible but it's nothing unique to the Soviet Union and it's not uncommon.
No, I think it was the archipelago tour where millions of people got to stay in remote islands but to their dismay never got to leave but they did get to write birthday cards to the steel man.