Definitely. Changes in the environment (new geographic isolation) will drive rapid evolutionary change, as evinced by the cichlids of Victoria lake. The converse is also true - a stable environment will drive slow or zero evolutionary change, especially in asexual organisms.
Agreed. A species that looks similar to a fossil we found dated 20 million years back is not evidence of "no change." Indeed, many of the more important genetic changes (homeostasis, immune system evolution) leave no skeletal traces.
The reason a changing environment and a routine environment induce different rates of change is the environment sets the potential for the DNA to change. This works similar to the brain. If one moves to a new place, a potential is created to adapt. If you remain long enough, you start to assimilate and narrow your options into a routine. Nature tends to recycle schema with the DNA under similar pressure, conducted from the environment to the DNA.
Creationism is misunderstood. Creationism is about the rise of modern man, with will power and choice. Human willpower and choice caused artificial selection to appear, along with natural selection. Good examples are domestic dogs and cats. The path of hundred of breeds of dogs and cats are no longer connected to natural selection, but human selection standards defined by cat and dog clubs. Even your favorite tomato plants are based on human selection; both heirloom and modern. Humans will create environments, that narrows selection to very specific human parameters; lab mice.
Beginning in Genesis, modern man with willpower and choice, caused an artificial selection to appear in nature, that would move parallel to natural selection. Lawns with Kentucky Blue grass is not natural, but artificially selected. Once you form cities, the trees are often planted by man who also selects the type and the exact spot. Genesis is the time=0 of a different clock, that runs parallel to natural selection, and often supersedes it, through choice and consequences.
These two paths are often confused. Humans are not just objective, but we are also subjective. Subjectivity adds a randomizer wild card, that can defy natural logic.The style of many dog breeds is not always based on the natural logic of nature; survival. The choice of a dog is often subjective/randomized to style, tastes and fads. This parallel path may be the unconscious basis for the random assumption behind modern evolutionary theory.
Say you were Noah and had to pick two of each animal. Could you pick the same as natural selection? We don't know until after the fact. Would you pick pretty, large, friendly, colorful, or would you have the time to watch each species, to make an educated choice, with only a few month available to pick all; artificial selection.