How did Lex Luthor find out about Superman's identity in comics?

Yes, sometimes he does. It depends on the specific comic storyline and continuity.

Yes, Lex Luthor knows who Superman is. He's been a long-time adversary and is well aware of Superman's identity and powers.

Comics often use various creative plotlines to deal with Lex Luthor. Maybe he gets defeated in a big battle or is outsmarted by the heroes.

Lex Luthor's age isn't fixed in the comics. It can change based on the creative direction of the writers and the era of the story. Generally, he's portrayed as an adult in his prime, often in his late 30s to 50s.

Yes, Lex Luthor was responsible for creating Doomsday in some comic storylines.

Yes, Lex Luthor is often depicted as bald in the comics.

Lex Luthor's hair loss in the comics was often attributed to various factors. Sometimes it was a side effect of a dangerous concoction he created in his labs, or it could be linked to a confrontation with a super-powered being that had a lasting impact on his physiology.

Comics got rid of Lex Luthor as president through various means. Maybe a plot twist exposed his corrupt actions, or a powerful superhero found a way to prove his misdeeds and force his resignation.

Bruce Wayne defeated Lex Luthor through a combination of detective work and technological advancements. He uncovered Luthor's secrets and used advanced gadgets and his network to expose and undermine him.

Well, Lex Luthor's death varies depending on the comic storyline. Sometimes it's due to his own schemes backfiring, other times it's at the hands of a powerful foe.