Thanks for a detailed feedback!
Monster (in it's true form) doesn't show up until the very end or until a certain conditions are met. Things and limbs you saw throughout the game are actually just harmless screamers to spice things up. The only clue of who is a doppelganger besides dialog is a TV broadcast that triggers automatically and gives away general info about the suspect (sex or maybe clothes). Sorry for a partly misleading description of the game.
As for the police, the reason why it can be called only once is that it arrives before the intended ending of the game and calling it several times would break the game. Calling police on the right person is a winnig condition and therefore should not be something you are supposed to do on the first playthrough or by a random chance.
Several similar anwsers is a bug and not a sign of a doppelganger. It will soon be fixed with a next update.
Also you didn't mention controls. Were they intuitive? Most of the people who we saw play this game seemed to have trouble interacting with ingame systems.
Edit: Game received an update. If you are still interested in playing we suggest to play on updated version. It fixes some game-breaking bugs and changes control scheme.