Knowing that everything is always in perfection and that the nature of the play is spontaneous unfoldment, does the Infinite care how the play unfolds for itself? Does the Infinite have a care in the world?
The purpose of life as an evolving expression of the Infinite Itself, has been discussed in more detail in the Premier Webinars, specifically because the purpose changed from self-examination to developing a means of self-communication.
As I recently mentioned, the Infinite is like an infant in Its developmental stage of embodiment. An infant goes through challenges during different stages of maturation.
First, it has to learn how to control its body parts (like picking up its toy rattle, or holding its bottle) — the stage of self-examination. Then how to say 'Mama' or 'Dada' (the stage of developing language).
You ask: Does the Infinite have a care about how life unfolds? Well, then I must ask: Does an infant? And the answer is no. Because an infant lives in the moment, not caring about yesterday or tomorrow. The infant does care about the quality of the moment — does the moment fulfill his or her needs or is it uncomfortable?
So no, the Infinite possibly doesn't have involvement in how the big picture unfolds — living only in and for the eternal moment.
The Infinite Has Preferences
Your second question is more complex and we cannot know for sure if, at this stage of development, an infant cares about anything at all, since it is in a state of surrendered trust of the evolution of life. It does not fear, because it cannot imagine life not supporting it.
But It does have preferences — an infant prefers comfort over discomfort. For the Infinite it would mean:
There are two ways of growth. One way is through building strength by overcoming opposition. Another way is through inspiration — by finding those things in life we feel inclined to reach for; those things that move us to try and include in our life. (Because love is the desire to include, we could describe an inspired life as a life that embraces that which evokes love.) The preference of all beings is to learn by reaching for that which we love, rather than that which we have to endure and overcome.
There are times when some discomfort has to be endured, but I believe that the Infinite seeks to refine the concept of what is 'perfection' by learning through inspiration (embodied by angels) rather than the pain of forced change (embodied by demons). So by having preferences and learning how to manifest them, one could say that the Infinite does care about how Its development takes place.