WOW EVERYTHING? I mean I'll summarise but I think the fun of it is finding info for yourself.. They're also pretty much entirely separated from the main Guilty Gear lore atm so I think scrounging for info is pretty easy.

Basically Paracelsus (Key Guy) was an axe named Flament Nagel, the "Sanguine Gale" and was defeated by Slayer (Vampire, also wife guy) and left to rot for an amount of years I don't currently remember.

A.B.A (wife) is a homunculus who's creator made her and bailed so she was left alone for 10 years. Her big thing is keys because they represent freedom to her, she found Flament Nagel one day and renamed him Paracelsus, after her creator. She takes a liking to him because he looks like a key and iirc he also starts to look more like one too because he molds himself to what the user wants.

She got attached to him and somehow they're husband and wife. I think the core of it is that they're both maladjusted "people" learning what it's like to live and in strive's arcade mode they're learning to respect each other, A.B.A realises she's being terrible and Paracelsus turns into her favourite colour 😭

I recommend watching the strive arcade mode cutscenes I think it does a pretty good job of summarising their entire deal and their road to getting better. Most other info I get is from the wiki and pieces from reddit ^^