In Homelander x Starlight fanfiction, one common theme could be the struggle for Starlight to maintain her integrity in a world dominated by Homelander's influence. Writers might create scenarios where she tries to change him or at least limit his more tyrannical tendencies. Another aspect could be the star - crossed lovers idea, where their relationship is doomed due to their opposing positions in the superhero world.
One popular trope is the 'enemies to lovers' trope. Given their different outlooks and Homelander's often villainous actions, this is a common way to build a relationship in fanfiction. Another is the 'power imbalance' trope, where Starlight has to deal with Homelander's overwhelming power.
One popular plot is the discovery of a common enemy that forces Superman and Homelander to team up, despite their differences. Another is a battle for supremacy in a world where both exist, with different factions taking sides. And then there's the plot where Superman tries to reform Homelander, seeing the potential for good in him.
Well, it depends on how the fanfiction is written. If it's a more 'grounded' version where Homelander's public image and mind - games play a big role, he could potentially gain an upper hand. But generally, Superman has more raw power. He can move planets, and his speed is almost limitless. Homelander is strong and has flight and heat vision too, but Superman just seems to be on a whole other level in terms of pure power.