Answer to last riddle: The detective payed no attention to the man across the river because he didn't do it. He knows this because anyone who jumped in the river and tried to swim would drown because it's a very deep fast flowing river. Even if they managed to make to the other side the man would be farther down river not directly across it. The guy is the criminal because if he wasn't he wouldn't have tried to blame the man who clearly hadn't committed the crime.
What's at the end of a rainbow.
