Your first assertion is addressed, and, unfortunately, invalidated in the series that I recommended.
The formation of the moon, a “lucky strike”, is just one of the thousands (so far) of “coincidences” that are required for life here. Again, especially in Privileged and Case For, they address this. That was just one example.
Your assertion that planets/stars form and collapse all the time is addressed, and isn’t quite relevant, either. The timeline is one way, and the possibility of rocky/metalic planet formation, plus the absolute right star type (type G yellow is ideal, and RARE, ie, near unique), could only occur during a specific time since the big bang.
Well, I did prove that the opportunities for the probabilities are infinite.
As for the (let’s say, humans) typing out Shakespeare, well the (humans), and Shakespeare are a linear extrapolation of the first chemicals that formed lifelike molecules, and gained complexity over the generations to form the variety of life, as seen now (this, if you believe in evolution).
So, what I’m trying to say is that the monkeys needn’t produce Shakespeare by chance. All that needs be done, to produce something as an alternative, and more/less impressive achievement, is for the situations that lead to the formation of simple lifeforms, to occur again. This, is not as astronomical in probability, when compared to sets of monkeys duplicating Shakespeare.