"Do with you life" uses "life" to refer to your long-term future experience while living--how you will spend your time, what goals you will pursue, etc. It's how you will use your life.
"Do to your life" would commonly be used in a very negative way (unless you explicitly qualify it as you did here), referring to some impending change to your existence. For example, taking an action that would destroy your future prospects (or in this case, open doors to better prospects). It's an act upon your life.
What is there to do with my life to make it better?
This would refer to major choices about actions or direction that would make your existence more meaningful or enjoyable; how to best use the time available to you during life.
What is there to do to my life to make it better?
This is a non-typical way to express it, but it would refer to taking a specific action now to radically change the trajectory your life is on and the potential opportunities that could be available to you.
Your second set of examples would be similar. "Do with it" refers to the manner and purpose of how you use your time. "Do to it" refers to your actions that change your opportunities.