Regarding kill moves :
Fair has always been the bread and butter of Peach's killing kit. As said earlier, Fair is very predictable and if you whiff it's very punishable and if you hit it on a shield then you lessen its knockback.
I think the best application of Fair is with ground float and to use float to perfectly space it. So if someone is rolling backwards or trying to recover, using float to go backwards or forwards to perfectly land a Fair as they land/come out of roll is a really efficient way to use it.
The other reliable option is Tennis Racket. If you sweet spot it, or even if you land it, it sends people flying horizontally off stage where you can harass with turnips or set up really good edge guards. Frying Pan is good for damage, and Golf Club is good to poke from range, but IMO Tennis Racket is a very very solid option for killing people. Now Peach's F-smashes come out in a certain order so you can hold the Tennis Racket for when you really need it.
Other options include B-Throw at edge of stage, using Toad, a quick Nair etc. But unless you're 150% + then they won't outright kill. Peach's style is more about using aggressive aerial game/edge guarding to gimp people out of stage rather than land a killing blow that will eliminate them outright. Yes, Fair can do this, but at lower % you'll find good opponents play around your Fair and mindgame you while you stay predictable.