Homelander does die in the Boys comic. It happens due to a combination of factors including his own actions and the opposition he faces from other characters.
In the Boys comics, Homelander's story takes many twists and turns. He battles with his own inner demons and external enemies, and his fate is quite complex and unpredictable.
Homelander dies in the Boys comic when he's finally overpowered by a coalition of characters who've been working against him. It's a dramatic and conclusive end to his tyranny.
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.
The 'brainsurge boys vs girls story' could cover a wide range of topics. It might be a fictional account where boys and girls are in a battle of wits. Perhaps it's set in a school environment where there's a quiz competition, and the boys' team and the girls' team are competing. Each team has its own strategies based on what are perceived as gender - related traits. It could also touch on the social pressures and expectations that boys and girls face during such a competition. The story might end with a lesson about how both genders have their own unique capabilities and that cooperation can be more beneficial than just competition.
I'm not sure specifically what the 'brainsurge boys vs girls story' is about without more context. It could be a story about a competition between boys and girls in some sort of mental or physical challenges.