In all honesty? At this point, if you are not able to ride independently, I would be concerned that anything you do on the ground might backfire and make problems for you.
When you work with horses but know little? The horse may begin to take advantage of you in ways that you don't realize are creating a problem. Disrespect, crowding, undesirable behaviors. All of that can make some major problems under saddle.
Groom, but all of the game playing and exercises? I'd leave alone until you have a better grasp on what you are doing and on how to read horses.
Horses make me a better person.