I'm not sure if this is even possible, but is there a way to extract the keyframes from an FBX animation? Basically I thought I could download some FBX animations from Mixamo, then tweak the keyframes - but it seems the keyframes don't show up in the animation editor? Or am I waaaay of and this isn't how FBX works?

you can try the labs fbx character import
and pipe all 3 of the ports to a joint deform