I'll address the "spontaneous pair production" (SPP) question first.
SPP specifically has been observed in a vacuum on many occasions. Out of nowhere, a pair of particles springs into existence, one an ordinary particle and the other its corresponding anti-particle - e.g. an electron and a positron. The two particles each have non-zero energy in that they move apart from one another. Their energy, however, balances in the sense that even though the particles are moving, adding the vectors that describe their movement will result in a zero sum. Their charges will be balanced. Their quantized spins will be balanced. Since one is matter and the other is an anti-particle (i.e. anti-matter) their masses balance to zero as well. But once they interact with something, they are detectable and, thanks to that interaction, they become differentiated from one another. I would LOVE to have enough money to be able to give you a full demonstration, because that would mean I could afford a high-precision particle physics lab. But as I am retired, I think I'll take a hard pass on the request for a demonstration.
Doc, seeing (understanding) is relative to one's perception based on experience.
Arthur C Clarke is noted for his "three laws" (not to be confused with Asimov's Three Laws of Robotics). The third law is simple:
"Any sufficiently advanced technology is indistinguishable from magic."
The corollary is that if you see something and think it is magic, your science must not be sufficiently advanced to understand it.
Miracles don't exist. Scientifically unexplained events, however, CAN and DO exist. (In line with another of Clarke's Laws, I am not denying the existence of the unexplained. I am denying a particular characterization of them.) Postulating an explanation of that unexplained event using magic and miracles is simply saying "I don't know so must be God." This is also known as "God of the gaps." The problem with Man is that it is hard for mankind to say "I don't know" and as a result they INVENT explanations - such as God.
That one biological mystery is mind bogglingly complex, made up of millions of elements itself that somehow execute the code within itself to duplicate itself (self replication). We are all made up of the exact same identical genetic code. The tree's have it, the fish, the birds, and the venerable bee's. It's the exact same code, just a different sequence. It would take a mountain of faith to believe that just happened from primordial soup sometime in the distant past by accident. Do not take that miracle for granted or assume that it is insignificant or normal. Think long and hard on this.
Nature has had BILLIONS of years starting from innumerable primordial ponds all over the world, where literally thousands of molecular collisions occur every second in every milliliter of your "primordial soup." That is being VERY generous to your position because in warm water, it would be a lot more than 1000 reactions per ml per sec.
How many milliliters were there for any one of them to come up with the answer? I don't know, but odds suggest "a lot." How many BILLIONS of milliliters were running thousands of molecular collisions per second? We have about 1.4 septillion ml in the ocean, but lets limit that to surface only, and I'll be VERY liberal - lets say 1/1,000,000 th of the total, or 1.4 quintillion ml for all of those ponds.
Then, if we have a billion years, that is how many seconds? (Roughly 31,556,926 billion seconds or 3 x 10^16 = 31 quadrillion seconds). So how many reactions? About 31 quadrillion sec x 1000 reactions/sec/ml x 1.4 quintillion ml) or 43 x quadrillion x thousand x quintillion possible reactions. That is 43 x 10^38 chances to get useful reactions. So there nature sits, iterating through millions - or billions - or trillions of solutions, and BINGO, one of them works.
Repeating part of your quote:
We are all made up of the exact same identical genetic code. The tree's have it, the fish, the birds, and the venerable bee's. It's the exact same code, just a different sequence.
Ah, but there is more to it than just that much. If you look CLOSELY at that "just a different sequence" you can even identify the genetic changes from one step of evolution to the next. Which is why we KNOW we are about 1.2% different (DNA-wise) from chimps. We can use genome mapping to SHOW the mutations that led from one species to the next. Merely nature iterating a little bit over what she already has to see what is new on the horizon.