Great post here.
As Astargath says, none of these "mathematical" or "irreducible complexity" arguments make any sense.
You might believe that they somehow disprove evolution, but actual physicists and mathematicians disagree with you. That is because your arguments are flawed.
There is no physical, mathematical or biological reason why a single common ancestor (LUCA), couldn't have spawned all life on Earth. You might believe it not to be so, and no-one knows exactly how it happened... BUT there is no scientific reason that it is not possible. And don't forget, we are debating the evolution of LUCA, not it's origin.
Your evidence to the contrary is flawed, and every biologist, physicist and mathematician knows it.
I myself study biology, and your arguments are flawed on a basic level. Not only that, when you are challenged, you resort to saying "well we don't know for sure that the laws of physics were the same then..." or something similar. This is not how science works - we don't just disregard results because we think that physics might have been different at a certain time. Assuming such changes, makes all results erroneous, and therefore makes the scientific method erroneous. So if you want to put your faith in such speculation, you cannot by definition make any argument relying on the scientific method.
To do so would be a logical fallacy.
Saying a single common ancestor could have spawned all life on Earth, what do you consider an ancestor? At what point do we come from something that is not an ancestor such as the atoms. Are we considering plants being our possible ancestors? What about dolphins?
If we cannot disagree with what we know about science now, what about the science that existed in the past that does not today; such as, the building of the pyramids or finding the creation for beer?