Re: Sword tip movement
To the OP,
It sounds like you're trying to steer the cut. Rather than worrying about the tip, visualize the target, whatever that may be. Then cut to the target. Your sword will straighten out.
Also, there's a tendency for one's dominant eye to pull the sword off-center. For example, I'm right eye dominant, so if I try to center the sword visually, it'll tend to go to the right of my center. One centuries old fix for this is to then think about cutting along the line of the opposite nostril. If you're right eye dominant, think about cutting along the left side of your nose.