I think the burden of proof relies on those to connect micro-evolution with the introduction of new species and previously non-existent genetic information.
Funny thing, that. The theory of evolution (as opposed to the purely artificial concepts of micro/macro evolution) already does quite an effective job of explaining and connecting how species change with how they diverge into new species. At least, assuming one isn't bound and determined not to see it.
I mean, I don't think that the explanation "Macro-evolution is just micro-evolution over a longer period of time" is valid based purely on its own claim.
If it were just a claim, then it wouldn't be. But the problem for people like you is that it's a claim that's supported by pretty much every bit of evidence we've been able to unearth.
Do we actually know how dinosaurs grew feathers?
The same way birds do, I imagine, since it's becoming more and more clear that birds are the distant descendants of the dinosaurs that weren't wiped out all those millions of years ago. The similarities are just what we'd expect of extremely distant descendants of something that lived that long ago.
Without just saying "evolution did it"? Like the actual process that had to happen? I don't think its reasonable to view changes in degree and changes within a species and claim that macro-evolution is just the same thing and to just leave it at that.
And I don't think it's reasonable to get overly pedantic about something and say, "if you can't explain the exact process, how do you know
evolution is responsible?" That's just ignorance masquerading as inquiry - a way to exploit the fact that we don't have total, 100% knowledge about something to justify claiming that something had to have made all organisms pretty much the way they are now. What we do know is that evolution explains the divergence of species far too well to just dismiss without active contradictions that would disqualify it.
Are there any current examples of micro-evolution that, given enough time going in the same general direction, would eventually lead to the introduction of fundamentally new structures, organs and/or processes within an organism? Have we even observed the shred of the beginning of a macro-evolutionary change?
Maybe if you stopped obsessing about the individual trees, you might be able to pay attention to the great big forest. Any individual change can serve as the basis for further changes, so long as it doesn't actively kill off an organism.
Can a bird really evolve into a different animal by taking the organs and body parts that it already has and simply making them bigger, smaller, thicker, thinner, brighter, darker, longer, shorter, more numerous, less numerous, more resistant to X, less resistant to X, etc.? Can a bird's beak really evolve into the exact same thing as a human mouth by simply getting stubbier, softer and applying various color changes?
Will it evolve into a different animal, like a horse or a pig? No. But that's not what evolution is about in the first place. Evolution is about divergence - organisms diverging into different species which are still related. So no, a bird's beak probably won't become the same thing as a human's mouth. But so what? There's at least one mammal species which has a bill, specifically the duck-billed platypus, and most likely others. So if some mammals can develop a bill (which is fundamentally the same thing as a beak), I see no reason that some birds couldn't lose their beaks, or develop teeth inside their beaks, or other things.
If humans went to a thousand different planets and developed a thousand different ways, their descendants a million years into the future would still fundamentally be humans. They would just have different characteristics based on their environments. If humans after a million years of evolution on a watery planet had mostly fins and flukes, instead of arms and legs, they would still be descended from humans; same goes for other genetic changes.
Isn't that what micro-evolution is? A change in degree?
That's exactly right; that's why this attempt to distinguish between "micro-evolution" and "macro-evolution" is pretty much entirely false. They're both the same thing; it's just that "micro-evolution" is evolution over a short period of time, while macro-evolution is evolution over a long period of time.
Could a single celled organism really eventually evolve into an elephant by taking the structures and processes that it already has and just changing the degree, ie: shorter/longer/bigger/smaller/thicker/thinner/brighter/darker flagella? Does a nucleus eventually evolve into a human brain through mere changes in degree?
It would take a long time, and more importantly, an ecosystem which didn't already have something fulfilling the role of "large grazing herbivore". Mammals wouldn't have evolved the way they did if the dinosaurs hadn't mostly died off, after all. But trying to draw a distinction between changes, as if a couple of genetic changes is fundamentally different from a thousand or a million, is a pretty dishonest way of looking at things.
Do we have any examples of micro-evolution that doesn't just use pre-existing (as in already existing in the world, contrary to being completely new) processes/structures/organs/etc.?
Seeing as all evolutionary changes ultimately spring from DNA, which is the ultimate in "preexisting" when it comes to biology, most likely not. But that won't help your argument That aside, we're still just scratching the surface of what biology is apparently capable of; trying to use our lack of knowledge to justify a preexisting belief that organisms couldn't have evolved from very simple origins is one of the most ignorant arguments it's possible for people to come up with.