Flickering - strange frames in animation.

Hello!
I have two problems which may be related to how I'm doing animations (wrongly I guess). The first one is that I get strange frames in one of my animations. The animation is a humanoid character breathing - the idle one. His left eye goes wild and spins around for a few frames regularly every breath. The model and animations were built in Blender. The animation itself obviously has no eye flickering in Blender, but it is there immediately in unity in the preview window. I had issues previously with the animation transitions, but I suppose it cannot be that if it is visible in the preview window. The rig is configured as a humanoid and there are eyelids, controlled by bones.





Here's a link to the pictures in Onedrive:
https://1drv.ms/f/s!AiAFpAZgCJjJj9EskMKKOImMECrDQw

My 2nd issue (which probably deserves a 2nd question but I will briefly describe anyway as it may give clues) is that at the end of one of my animations the character reverts back to his original position but for one frame only and my code isn't changing the position on that frame. The animation in question is static and I manually transform the object using curves and code.

Thank you for any and all help, pointers and suggestions on places to look. Any questions, please ask. Thank you!