Hansen vs. Predator is similar to Hansen's Famous mid-2000s era report series for Datline NBC called "To Catch a Predator" which was originally started to alert parents to the then new technology of Online Chat rooms and the threat of sexual predators targeting minors online. The reports were wildly popular at the time as each one had an unstaged "Just when we thought we've seen it all" moment where the production crew is shocked by the situation unfolding (one of the first was a man who got caught twice in the same sting. Another memorable moment was a man who was caught in two separate stings (he was on bail for the first one when he got picked up in the second one)).
The methods are largely the same. Hansen himself does not pose as the child in the chat room, as many of the suspects engage sometime prior to the sting operation. Those posing as children are typically volunteers with non-profit organizations that were dedicated to finding people who were targeting children. They also are not approached by the men first and only entice further once they are engaged by someone and repeatedly make the decoy age known to the suspect. It should also be noted that the crime most of the suspects are prosecuted for are related to the online conversation and police do not need them to show up at the house. The benefit is they do not have to track down the suspect AND by showing up at the house, they show further intent. With exception to the first two Dateline reports, the police are always working in conjunction with Hansen's staff and the non-profit (In the case of the first two, Hansen's team did turn over all evidence to the cops following the sting, however, that guy who got caught twice in the same sting convinced the team to do this with the help of local police, who had been skeptical up until the first few shows aired.).
At the time the actual interview is made, the suspect is not under arrest ("But he soon will be.") and Hansen presents himself as a stern authority figure and instructs the suspect to "have a seat right there" and proceeds to interview them. Hansen will tell the truth if he's asked if he is a cop ("I'm not a cop.") but will dodge the issue of who he is otherwise ("We'll talk about that in a minute."). Typically, the suspect, on hearing that Hansen isn't a cop, assume he's the decoy's parent. By the third entry into the "To Catch a Predator" series, a handful of suspects will recognize Hansen on sight and react in various ways (some run without question, others will cry or scream in terror, more than one admit they watched previous entries in the series and will act almost like fanboys meeting their idol.). At either rate, when Hansen is finished with the interview, he'll tell the ones who don't know what's happening who he is ("I'm Chris Hansen with [Show name]") as the camera crew comes out and reveals this is going to be broadcast on national TV. He offers them a chance to give some final comments now knowing everything is taped and the directs them to leave the house ("You are free to go") which the predator will take up on the offer ("But he won't get very far") at which point the suspect is swarmed by the police and arrested and Mirandized.
Because Hansen is a private citizen (with one exception, where the county sheriff's office deputized Hansen's team because state law required all operations of a sting be conducted by Law Enforcement Officers (LEO)) and at no point during the show the interview is the suspect under arrest. Additionally, he is not in violation of 2 party consent to recording in states with such laws because all 2 party consent laws make exceptions if the recording features a party to the conversation discussing their participation in a crime AND are only good when one has a reasonable expectation to privacy, which they don't have on someone else's property. The portions of the show where the suspect is talking to the real cops is also legal to use as the recordings are released to the public as part of the open trial requirements, and are by law public domain upon creation as are all government documents in the United States.