Thought provoking, but you're overlooking somthing:
None of your events are independent. Thus, the formula for Probability(first event happens and sencond event happens) is NOT Prob(1st event happens) x Probability(2nd Event Happens). Instead it's Probability(1st event happens) x Probability(2nd event happens GIVEN 1st event happened).
Note that the given can be expressed either way, so for example, Probability(our solar system can support life AND I'm alive) can be expressed either as Probability(our solar system can support life) x Probability(I'm alive given our solar system can support life) OR Probability(I'm alive) x Probability(our solar system can support life GIVEN that I'm alive).
Those two probabilities above with the swapped givens are mathmaticially equivalent, but notice that in the second one: Probability(I'm alive) x Probability(our solar system can support life GIVEN that I'm alive), the second probability equals 1. ie: the solar system MUST be able to support life given that I exist.
That means that if you run the math with the conditionals in place, a lot of the events you're counting probability from disappear.
Then, you have to understand that the probability "I" exist, assuming my parents made a child is 100%. Why? Because the probability that I have SOME genome, given my parents had a child is 100%. While the probability I get a specific genome is an incredibly unlikely event, you're looking at a posterior probability, while in fact, if I had a completely different genome, it would still be "my" genome. It's impossible for me to have any genome BUT mine.
A lot of your probabilities shake out in issues like that too.
So, in the end, your probabilities are way off for various mathematical and philosophical issues, but that didn't stop it from being a fun video with an uplifting message, so I'm more nitpicking because probability and nitpicking are "my thing" to do. What's the probability of that? :p