The "keyframe for every single frame in the animation" part of your question "is a feature, not a bug": That is how Blender outputs an FBX.
In object mode, select your armature. I imagine you may not be able to see it unless you turn on Xray.
Now go into pose mode and Blender's Animation screen set up.... or, I find this easier, anyway:
Your dope sheet will show you which bones in the armature have actions keyframed to them. Although Blender creates a keyframe for each frame, it does not create one for each bone -- only those bones that have actions associated with them.
In the NLA editor, you can turn this set of keyframes into an action strip, and you can B box select and simplify.... but it is still less elegant than what you undoubtedly had in your original Blender file.
Regarding names and axis... does your file look like this?
If that's what you are seeing, you can turn them off under the Armature panel.... but I have seen weird issues with some FBXes (more often scaling and orientation than naming)... and frankly I typically just hack at them until I get what I want... That is not really an answer... just what I do.