I’m sorry for the confusion. Have you tried slowing down the playback to 0.5x? If not, check out that setting in the video player UI on the bottom-right side.
As for the binding of the eye:
1. You need to parent the eyeball object to the armature, not using automatic weights – just plain parenting.
2. Then add a vertex group on your eyeball object that matches exactly the name of the bone you’re binding to.
3. Select all the vertices of your eyeball object in edit mode and assign them to that vertex group with a weight of 1.