"The moths evolved to become dark in order to match the background of these trees." "Those guppies evolved to be very colorful, over the course of just two years." "Over ten years they evolved significantly shorter legs."

Remember, the variation already existed. There were already white and dark months in the population and natural selection caused increase or decrease in the ratios. The black moth did not evolve into white. The variation for short and long legs already existed. Short legs probably increased reproductive fitness in once case and not the other. Causing the number of individuals with certain trait to increase or decrease. My professor has repeated this the entire semester and she wants us to never forget that mutation is the only source of variation. If the variation is not already present, natural selection cannot trigger it. This is how some species go extinct. Natural selection is one source of evolution. Also, distinction between micro vs macro evolution is important here. [0]

"But there's no reason to believe this. Why shouldn't they be adapting to our conditions just like any other evolutionary situation?"

Because natural selection doesn't cause variation. Mutation is the only source of variation. Variation must already exist in a population for natural selection to work on it.

"What she found was that in each case they had changed. The lizards in the city had evolved longer legs—presumably useful for hanging onto broad surfaces, like walls—and they had evolved bigger toe pads—again, presumably to hang on to the smooth surfaces in cities. "

Giraffe's neck get longer with usage is a Lamarackian theory which is an outdate model because we know only changes in the sex genes are passed on to offspring. [1]

"Evolutionary biologists have become very interested in recent years in a higher-level analog of this, and that is the mixing of different species—hybridization—when two different species interbreed and are able to successfully reproduce."

Depends on your definition of species, there are many. [2] The biological definition is one where if they fail to see each other as potential mate naturally and produce sterile offspring, they are different species. So I am not sure which of the 13ish popular definition I am supposed to apply to this. And genetic definition always considered more variations to be good. So that one won't work here either.

"When wolves were around, coyotes were small. But, you get rid of the wolf, suddenly, there's this great opportunity for coyotes to evolve to get bigger and eat the bigger food that the wolves aren't taking, such as deer."

There is no selective pressure so both big and small coyotes would increase in number. I know where this is from though, we watched the video in class. It's called "How wolves change the river."[3]. It's really good, please watch it.

"Are they just mutations for larger size that then get taken advantage of by natural selection? That can happen, it might play a role, but it seems more likely in the case of a coyote that it's the result of hybridization"

So the author is aware of the concepts but it just brushing them off?

"Think about weightlifters, for example. If you spend your life lifting weights, you'll develop very big muscles and thick bones. But that is not a genetic change. You have not evolved. "

Correct, it means that variation "genotype[4]" is already present.
"Those differences will not be passed on to your offspring."

Incorrect. there is a change that the genes that allowed for larger muscles in you will be passed on. Just the "phenotype" won't pass. The kid wont be born with big muscles, but like you, if he exercises, he might get similar muscle.

I don't see citation for any of the claims on the articles. If I missed it, I apologize. I am not an expert and these are just my opinions based on my very limited understanding on the subject matter. Feel free to correct me.

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[0] http://evolution.berkeley.edu/evolibrary/article/evoscales_0...

[1] http://natureinstitute.org/pub/ic/ic10/giraffe.htm

[2] http://evolution.berkeley.edu/evolibrary/article/evo_41

[3] https://www.youtube.com/watch?v=ysa5OBhXz-Q

[4] https://en.wikipedia.org/wiki/Genotype

Edit: Added white space for clarity as suggested.