Alright, I think the anime might have cut out a bit of dialogue, but here are the answers:>If Rodd was a real king why is military police threatening him?
Not him. >Or he just stage all this to play a victim before his daughter?
The fateful night that Rod went to go get Alma (Historia's mom) and Historia herself was the same night the Assembly (The bundle of people you saw dictating Erwin's fate and where you also saw Kenny at one of the sessions in Episode 11) sent Kenny and his squad to "cleanse" the royal family of the dishonor of having a mistress and a bastard child. Unbeknownst to the rest of the Assembly, Rod's entire family got massacred by Grisha Yeager and the Founding Titan was lost from Reiss' control. Rod decided to strike up a deal by sending
"Krista" to the front lines. Thus saving her, in a way.>Then why he sent her, such an important person to the frontline fight titans
He attempted to monitor her through the Wall Church. Her royal blood was very important, but the Founding Titan was the most important thing.
He also only told the Assembly about losing the Founding Titan and his family after Eren transformed in Trost (Afraid of losing power). Which is why the MPs and the Wall Church were trying so desparately to get Eren "back".