Take it easy--we're doing this the slow way, top-up way, not the "gotcha" way

I am not trying to justify evolution at this stage, at all. I'm doing it this way because each of the sentences in your first post were legitimate questions that have been asked by biologists before so I wanted to illustrate that you guys are not the only ones asking these questions, and show you how they can be answered. I want this to be a dialogue where everything is fully explored before we go on to the next stage. In other words--let's talk mutations, DNA and genetics now. Let's not jump into evolution yet unless we
really understand the mechanism. I mean, think about it--if I tell you something can happen, you ask how, and I tell you "oh, some mechanism you don't understand and I can't explain," of course you're going to conclude that it might as well be magic. That's completely reasonable, if you're a bottom-up approach type person (I know I am, and I suspect you are too).
So, let's finish talking about your post first. Maybe we'll touch on the structure of DNA, the structure of the chromosomes, how gene transfer happens, etc. At the very least, I figure we'll cover some really cool stuff--I find microbiology really cool.
Anyway. That aside, sentence 2:
See, this is exactly the sort of thing we can clear up here! It is actually surprisingly subtle how tricky statements in genetics can be.
First off... does DNA mutate randomly? You actually hypothesized it does, which is interesting--right off the bat it's a statement I might jump on if I were skeptical about the process. It's almost a philosophical question in some ways. If it didn't mutate randomly, just "chaotically," what would it mean for genetics? I've talked to a few people about this and the consensus answer is: it basically doesn't matter whether mutations are really random or not. But clearly "true randomness" and "completely predictable" are a gradient. And surely something
this important to the evolutionary process has to operate within very tight bounds. Surely someone has done the math that will let us know what the constraints are?
It turns out that to answer this question effectively we need to understand the different ways DNA can mutate. Note--I am not saying evolve, nor that they do not evolve. I am only saying that they mutate
Let's start with some of the assumptions of present models for DNA mutation:
* All living organisms in the domain of interest use DNA for replication.
It so happens that we have yet to find a living organism that does not primarily store its genetic material for replication as DNA. I am not speculating about a cause for that here. As far as I know, common ancestry doesn't speculate a cause for that either. That's just a basic assumption of the theory. If it makes things easier for now, assume a creator did it
* All living organisms in the domain of interest have at least some form of DNA repair.
Again, it so happens that we have yet to find a living organism that does not have some form of explicit "DNA repair"--going back to the Wikipedia definition, "a collection of processes by which a
cell identifies and corrects damage to the
DNA molecules that encode its
genome." In fact, it turns out that even RNA viruses generally have a mechanism that works pretty much the same way. Again, let's not, for the time being, try to explain this--even if you think you have a really good one, let's hold off! It's enough to say that it's an assumption of our theory.
Now let's talk about another thing before we begin in earnest. It's one thing to say that all organisms have
some mechanism for replicating based on DNA, and
some mechanism for error correction. But the specifics of these mechanisms can vary significantly in complexity and the added complexity can be really, really confusing when you are starting from scratch. I totally get what you are saying about not being interested in bacteria (prokaryotes), so obviously you'd prefer to start with eukaryotes. But prokaryotes are a
way easier to understand and still get all the same concepts across: think of prokaryotic genetics as training wheels for eukaryotic genetics. If you want to press on with eukaryotes anyway, we can do that, but it's just going to be
tough.
Provisionally, I will start us off talking about prokaryotes, so apologies if that is enough to get you to disregard this post--but I promise you, I'm not doing it to mislead
One final note of warning. Often in biological texts you will see statements that seem to be making claims that an organism, or a protein, is itself "thinking." An example is above, where the claim is made that a cell "identifies and corrects" genetic damage. This sounds like intelligent behavior, doesn't it? It evokes images of someone sorting a deck of cards, or scanning two copies of a textbook looking for inconsistencies--not just intelligent activity, but downright
academic. I just want to clear this up--all such descriptions, at the cell level, are just a way to anthropomorphize chemical reactions to make us feel like we are in familiar territory. The microbiological world seems like an alien landscape a lot of the time. Water doesn't act like water. Electric charges are powerful things. Putting something on top of something else--something that we have to work
not to do in the macrobiological world--can be nearly impossible. So when we talk about processes that work like this, please understand that we have not even once seen even a hint of intelligence at the cell level. I hate speaking in terms of certainties so maybe some other microbiologists can tell me if I am wrong, but I do not think even one process at the cell level has been discovered that is not modelable as a chemical reaction, augmented (in rare cases, like photosynthesis) with quantum electrodynamics. "Real science," as you put it.
Now. What could cause DNA, a molecule, to mutate? Here are the four mechanisms I know of, stolen blatantly from Wiki:
(1)
spontaneous mutation - DNA is a molecule, made of chemicals--so naturally it is subject to the laws of chemistry. There are four major ways we see DNA break down, "spontaneously," at the chemical level. I hope you like chemistry, because molecular biology is full of it. There are four distinct processes listed for how this can happen, and my understanding is that these can occur at different rates, so please read these articles carefully for more information:
tautomerism,
depurination,
deamination and
slipped strand mispairing.
(2)
error prone replication by-pass. I'll just quote the Wiki definition in full:
(3) Error induced during DNA repair. As you can probably tell from these numbers, mutations definitely happen at a quite sizable rate. This is where those DNA repairing processes come in. Now, they wouldn't be very good processes if they have a
high error rate, but they do make mistakes sometimes. This is a place where the discussion benefits from talking about simpler protists, because they have a simple (and quite interesting) model for this. See
homologous recombination in bacteria.
My own take on it, since I hate to just link to articles: in biology, we call catalysts that are also (generally) proteins "enzymes." Sometimes a group of these enzymes will be "linked" together, but not with covalent bonds--the exact form of the linking can be rather complex, see
proteinprotein interactions. Such complexes can have very different properties.
In the particular case of homologous recombination in
e coli, a three-enzyme complex called RecBCD binds to one end of the DNA double helix. If you are wondering how it finds it--the way that proteins in the body work is an example of how cells can trigger precise, staged reactions without really being able to consciously control the reactions. While there may be signals (sometimes local) for more or less of a protein to be produced at any one time to be made, simple prokaryotic cells are flooded with proteins of all sorts of different types. So they "find it" by kind of just... floating around until they bump into something they bind with

Biologists, correct me if I'm wrong! But wait--don't lots of chemicals bind with lots of other chemicals, even ones you don't want? Yep! It happens all the time. There are a ton of errors going on at all times in every one of your cells. That's life--literally.
Anyway--so it binds to one end of broken double-stranded DNA. The double helix is "unzipped" by two of the enzymes in the complex (RecB and RecD). The RecB is also attached(ish) to an enzyme called an
AP endonuclease, which is a type of enzyme that
cuts DNA that "looks" damaged in a particular way (in a rigorously chemical way). And this keeps going until a sequence called the Chi site is encountered.
I have to go to get some work done so I need to stop for now, but the discussion is quite technical so please ask questions if you have them! Giving up on a concept because it's hard to understand is never a good idea--not that I think you will give up, but it can be tough to look at that many technical words at once and not wonder whether someone is playing an elaborate joke on the public

By putting your questions out in the open we can help make sure that you understand all the science so you can act in an informed manner.