This is too long to respond to all in one go without becoming unmanageable for people to read. I'm going to select first your comments about science in general, to see if we can reach an understanding on what science does.
You say the Geiger-Marsden experiment "proved" something by "mathematics". That is wrong. It did not. To everyone's shock and amazement, most of the alpha particles went straight through as if the gold foil was empty space, but a few bounced right back at the alpha particle source. This was evidence that atoms are mostly empty space, with a tiny core in the middle in which all the mass is concentrated - enough to make an alpha particle bounce back if hit directly. Mathematics was naturally involved in interpreting the observations quantitatively, but nothing was thereby "proved".
Consider Brownian motion. No maths here at all, just observation that smoke particles seen through a microscope jiggle about randomly. This is evidence for the "kinetic theory of matter" - the model according to which matter consists of tiny particles in random motion. But it is not proof.
So there is a reason why you keep on tediously hearing the same point that "science doesn't deal in proof". If you had understood this point you would not be saying that the Geiger-Marsden experiment "proves" something, or making inappropriate analogies with courts of law.
The theory of evolution has the same status in science as the kinetic theory of matter or the structure of the atom. All of these are "only theories" if you wish to characterise them that way.
They are not "facts", they are "models".
I am not disputing chemistry or any other branch of science that explores different facets of creation...per se.
My major gripe has always been the way evolutionary science is presented to young people, especially those still at school. There is nothing mentioned to them about the hypothetical nature of science's pet theory.
I look at the likes of Dawkins and Coyne and all I see are egos spruking nonsense with ridicule as their primary weapon against any dissent....."you will believe what I say or you'll be sorry you didn't'. I will hold you up to ridicule by making you appear to be a fool in front of everyone." I have always hated that approach.
The only "facts" in science are reproducible observations. The theories are not facts, for the very good reason that they are continually subject to revision in the light of observations that do not fit. In science, all "truth" is strictly provisional. Even Newtonian mechanics, trusted for centuries and still trusted by engineers to this day, has been shown not to work for the very small, or the very fast.
I understand all that....but that is not what I am arguing about. To say that "the only "facts" in science are reproducible observations" is to dismiss 95% of what science teaches about macro-evolution. There is no way to test macro-evolution with "reproducible observations". The whole premise of evolution is based on adaptation, which is based on reproducible observations"...but what cannot be reproduced is what goes beyond adaptive ability.....there is no way to prove that adaptation can go beyond what is observed in a lab.
Are you OK with this so far?
Are you with me so far?
And that risible "just a theory" of evolution, predicting that a link would be found between whales and land mammals:-
Pakicetus - Wikipedia
And this is a case in point.....how much actual evidence is there that the creatures that are presented as intermediary species in whale evolution, actually are?
How big was Pakicetus? He is about the size of a dog.
How reasonable is it then to assume that this small land dwelling creature eventually became a whale?
Going to my favorite site....under the heading "The Evolution of Whales" it says.....
"The first thing to notice on this evogram is that hippos are the closest living relatives of whales, but they are not the ancestors of whales. In fact, none of the individual animals on the evogram is the direct ancestor of any other, as far as we know. That's why each of them gets its own branch on the family tree."
The evolution of whales
Do you notice something about this diagram? Look at the size of pakicetus (pictured above in relation to a human) and then notice the size of the whale at the bottom. They don't appear to be very different in size, do they?
Now look at the comparative size of the these animals.....
A human is in the bottom right hand corner. Now if pakicetus was much smaller than a human, compared to the size of the whale depicted here, where would pakicetus appear in this diagram?
According to Berkeley's Evolution 101, 'none of these creatures is a direct ancestor of any other'....Is that what the diagram conveys though? When you look at that diagram, what is it natural to assume? A line of decent.
It goes on to say.....
"These first whales, such as Pakicetus, were typical land animals. They had long skulls and large carnivorous teeth. From the outside, they don't look much like whales at all. However, their skulls — particularly in the ear region, which is surrounded by a bony wall — strongly resemble those of living whales and are unlike those of any other mammal. Often, seemingly minor features provide critical evidence to link animals that are highly specialized for their lifestyles (such as whales) with their less extreme-looking relatives."
So what is it that convinces scientists that Pakicetus, although not resembling a whale by any stretch of anyone's imagination, can be placed in a whale's evolutionary line of decent?......nothing more than a 'similar' ear bone. This bone "strongly resembles those of living whales". Now I don't know about you, but that stretches my imagination way further than an Intelligent Creator fashioning individual creatures out of the same raw materials and placing them in appropriate habitats that he designed for them. I don't see any creature in this line of decent as being related in any way to one another and Berkeley actually says so.
This is what I come across all the time. I check out the links people give me and find that they do not say what most people think they do. Its like the truth is hiding in plain sight.