Homelander's son doesn't become evil in the standard comic storyline. The focus is usually more on Homelander's own actions and the conflicts he's involved in rather than his son's moral alignment.
I don't think so. There's no indication that Homelander's son turns evil in the comics.
Not that I'm aware of. In the comics, Homelander's son doesn't have a storyline suggesting he becomes evil. Maybe it's different in some alternate versions, but in the main comic series, no.