Keyframing Bone Rotation in several modes: need help here !!!

Hi all,
keep in mind that I am still learning Blender…

I have an armature (rig of a belt). All bones are keyframed in Quaternion mode (and not any other mode). The exception is the Base bone which has also keyframes in other rotation modes (XYZ etc…).
I don’t know how this happened, I probably made a mistake at some point.
Two questions :
1)Does it hurt to have keyframes for the different rotation modes on the same bone ? Should I clear the keyframes in all modes except quaternions for the Base Bone?
2) For that Base Bone, when I go from Quaternions to say XZY, the belt is rotating and when I go back to Quaternions it doesn"t go back to its original location ? Only crt-Z will bring it back. Do I miss something here ?

Some pictures (Base bone selected in all):
Quaternions are keyframed


XYZ and other modes are also keyframed


Going to XZY mode rotates the rig (and doesn’t come back to its original location when going back to quaternions mode)