Nerfed Ilyria wins narrowly over Dark Willow
Because Ilyria doesn't fuck around and even with less powers she's still good against magic. And I think Dark Willow is overrated. Pre-meltdown Ilyria would have even less trouble because she controlled time and was even more restant to magic and pretty much unstoppable physically.
Angel draws Buffy
Hmm, assuming Angel, not Angelus and assuming further that both are motivated I'll have to call a draw. By "no weapons" I assume they'll fight somewhere where Buffy would be able to fashion a stake from something eventually... like one of those vamp nests where they inevitably have cheap wooden furniture. But this one is impossible to call, assuming both are at the top of their game. Buffy beat Angelus, but Angel circa S5 was a whole nothing level.
Wesley gets it done against Giles
Badass Wesley wins a narrow decision over grieve-stricken badass Giles. Both have understated magical ability but Wesley went to the bad place for a while and has shown a greater capacity for both brutal human-on-human violence and outright cheating.
Faith beats Connor
Faith easy. I think this one was answered for us - in the future Connor would likely win but during Connor's run on the show he was clearly Faith's prison bitch. "Break me off a switch, son. There's about to be a whoppin'"
Spike eats Gunn
Love Gunn, Gunn is great against vamps, but Spike is an older, meaner, better fighting vamp than the homeless-kid eating scrubs Gunn normally faces.
Principal Wood decapitates Doyle
Doyle was stronger and more capable than he let on, but Wood pretty much trained his whole life to kill vamps and demons. And really in the end Doyle wasn't much of a fighter, he just took a good neck snapping in much the same way Xander's main fighting strength was the ability to absorb a good beating.