In general, I think any definition of "superhero" that excludes non-powered characters like Batman or the Green Hornet or the Phantom is fundamentally flawed . . . . although the Scarlet Pimpernal and the Lone Ranger are definitely borderline cases.
Well, the definition I offered includes costumed characters who perform supernormal feats through technological means. The Green Hornet, at least in the TV series, had his share of fanciful gadgets -- the supercar with the silent engine and the "infra-green" headlights, the garage floor that flipped over to reveal the car, the Hornet Sting, the knockout gas, the UAV-style aerial probe.
As for the Phantom, I'd put him more in the "costumed hero" category, but he has enough trappings of superhero fiction that he could count as a superhero by a literary definition if not a technical, in-universe one. He has the colorful tights and mask, he has the secret identity, he has the trademark symbol, and he's a figure of myth and legend, The Ghost Who Walks, the man who cannot die. If "super-" can apply to anything that transcends normality, that's above and beyond ordinary heroics, then the generational legacy of the Phantom and the mythology that's grown around it (in-universe) could indeed qualify. After all, myths and symbols have their own power. (One could say that the Phantom was the first legacy hero.)
Hell, the Green Hornet is basically a contemporary version of the Lone Ranger, and he counts as a superhero.
Yep. The Lone Ranger's grandson, originally, though I'd imagine a contemporary adaptation would have to drop that or at least add a generation or two to the lineage. Though in the current or recent comics, aren't the new GH and Kato the next generation after the originals?
Does XENA count as a superhero series?
I don't think so.
Hercules might, since he was a demigod with actual superpowers, but Xena was basically a distaff Batman, an ordinary human whose effectively superhuman abilities were presented as the result of extreme skill and training. Okay, one can be a superhero without innate powers, but Xena didn't have a costume (per se) or special gadgets (just weapons, though the chakram seemed magical). She did have a sidekick, though...