Bye weeks are for the most part going to be chosen by the teams. They currently have the option of having it the week following an international game, if scheduled. Very soon there will be 16 international games every year so teams will choices in most all cases.

Schedules are for the most part based upon stadium availability. The final pairings are determined until after the Super Bowl. Events are prescheduled in stadiums sometimes years in advance. The use computers to generate the possible schedules based upon those and other factors. I saw a special on the making of the schedule a couple of years back. Very amazing!

As for the force behind a potential "rigger", what does that force have to gain? Now there are at minimum two people involved. What now do the additional parties have to gain? Vegas is actively involved in monitoring gambling activities to a degree that most would not be able to comprehend. Notice the number of players that have been "busted" by the league for a variety of gambling related activities recently? They were all reported by the gambling industry itself. I understand they can monitor things such as bank banking activities of individuals connected to the game, gambling apps, and other areas that can indicate questionable activity. Some of the players had other people placing bets for them and still got caught. Vegas is serious about anything affecting the integrity of the sport. They're making far too much money regardless of which team wins any individual game to have their cash cow toppled by any impropriety.