Billy doesn't kill Homelander in the comics. The interactions between them are more nuanced and don't end with Billy being the one to cause Homelander's death.
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.
Definitely. The comic version of Homelander is portrayed as having greater strength and capabilities. This is evident in his confrontations and the scale of his power displays throughout the comic series.