Can internet “officials” do an illegal search and seizure and record it all on a cell phone?

This sounds really fishy.... most law enforcement officers will identify themselves, who they are, and why they want to talk to you.  When they ask for consent to search your vehicle, typically they will ask something like, "is there any contraband in your vehicle.... like guns, knives, or drugs..." and then "do you mind if we search your vehicle?"  Officers are not required to read you your Miranda warnings unless you are in custody--but many will out of an abundance of caution.  Some will record things on their cell phones, but most will ask that you come to their office so that the interview will be visually and audiolly recorded.  Officers never take things "for no reason."  They have to have a reason to take things like your knives.  It really sounds like you were interviewed by two very unprofessional officers or by two con men.  You may want to contact your local police station and explain to them what happened... and see if these con men have been working others in your area.  They now have your background check form which probably contained all the info they need to use and abuse your identity.  IF these guys are legit, the police station may be able to give you more info on who they were and why they were talking to you.  If these guys are legit, then they can talk to you as long as you are willing.  They would not have been required to read you a Miranda warning unless you were in custody.  Even though unusual, they could record you with their cell phones; and they can search your car if you give consent....but to take things that belong to you, they would have to have a reason to believe they had been used in a crime or your consent.  You can request a return of the items from the agency that they work for if they do not have a basis (other than consent) for retaining them.