Your questions make sense. I believe the writers wanted the viewers to speculate on a lot of things instead of making conclusions for us. There are two Johans, one is the bad guy the other is the normal guy. I believe the "monster" Johan wants to kill the normal Johan (this answers your suicide question).
At first I thought the good part of him wants to kill the bad part (coz he says he should be shot in the head). Maybe at this point the good Johan understood that he needs to kill the bad Johan (this also answers your suicide question). Later he grows up and the bad Johan takes over. He creates a complex environment to start a war and to get himself killed by Tenma. I believe Tenma is dragged into this as the ultimate good guy who has to become a bad guy. Through out the series it's obvious that Johan is confident in turning people evil and maybe that's why he wants Tenma to kill him.
At the end when they conclude that he wants to kill everyone in that village/town to erase all evidence of his existence I thought that the bad Johan wants to kill the good Johan. Basically "Johan" the individual wont exist anymore. I guess what will remain behind will be pure evil. I think this is what ties in with the whole "experiments" revelation etc. The experiments were they try to create a certain type of person. The emphasis on the need for a "name" is through out the series. The monster wanted a name. But if you reverse that then it means a monster doesn't have a name. Which I think is where we find Johan. A person who needs to become a monster. He needs to lose his individually, his existence, his "name". So in the end he trys to erase that and become a true monster. (this answers your split personality issue). I think to a certain degree Nina knew this.
She probably didn't involve the police coz her goal was to find Johan and kill him. I think. There's a lot of speculation in this series.