No. Superman comics are mainly about his heroic deeds, saving the world, and his battles against villains. They don't contain erotic stories as it goes against the positive and family - friendly image of Superman.
Batman vs Superman's story involves a complex web of events. There's public pressure, personal vendettas, and a looming threat that forces them to either work together or destroy each other. It's a battle of wills and powers.
Definitely. Batman and Superman have long been featured in DC Comics, and the movie takes inspiration from those comic sources. It incorporates elements and plot points from various comic story arcs.
Superman's sexuality has been explored in different ways in the comics. In some cases, he has been shown to have attractions beyond the traditional heterosexual norm, suggesting bisexuality.