About Monaca involvement in this Killing game....
If Monaca is the mastermind and the one who killed people, then it will be simple and logical. But this is Danganronpa so it probably not that simple.
If we say that Monaca and mastermind are different person but..
A: She is working with Mastermind
While this surely explain how Monaca can free roam around the place with no interruption from the mastermind. However, I think Monaca is not the type who will work under someone order (unless that person is at Junko level). Moreover, she can control Monokuma and there is no reason why she has to hand over the control to someone else. If she need to work with someone, she probably on the top of the chain of command , but then that will mean she's the mastermind.
B: Mastermind and Monaca doesn't know each other
whether it is... Monaca unintentionally get caught in the mess but she finds it is a good chance to do something. OR Monaca found out about the mastermind plan in advance and decided to interfere it for her own goal.
The mastermind probably found out about Miaya being the robot controlled by (someone) since the first sleep time but then why he still let her in his game? Did Monaca hijacked the game from him? Why didn't mastermind do anything when they tried to contact future foundation?
Oh so many questions.