I agree with the bolded.
You are aware that this version of "Lex" is Alexander Luthor, right? That seemed to escape many people's understanding. This was an origin story for him. Not your atypical already-seemingly-perfect-genius type yet. Snyder was playing the long game with Luthor and Darkseid.
How do you figure that Wayne isn't a good detective in BvS...? Batman has never been perfect, but, outside of being manipulated by a maniacal genius I'm not understanding this statement. He was looking for The Portuguese since the beginning of the film. He found it. He meticulously planned every moment of the battle with Superman. He could've killed "a god". It was A+ Batman there.