Expound. How would creatures not changing over time be a problem for creationists?
Because creationists acknowledge the fact of speciation. Why some populations would change, and not others, is a dark mystery to them. But Darwin pointed out why natural selection would do this in unchanging environments.
Why would some creatures remain virtually unchanged from those found in the fossil record, while others changed radically?
Because, as Darwin pointed out, natural selection will prevent evolution for well-adapted populations in unchanging environments, and cause evolution in those where it's changing.
It's a puzzle for creationists, but Darwin himself pointed out the reason. If a well-adapted population lives in an unchanging envirionment, then natural selection will greatly slow down, or prevent evolution. Hence, living fossils are found in places where environments have not significantly changed over a long period of time. Coelacanths are a good example of this.
No, it's quite right. Where environments have not changed much (such as in deep oceans) we see very little change in many organisms, such as coelacanths. However, they have changed to a degree, even there. As you learned, the species of coelacanths living today are not found in the fossil record.
Even evolutionists acknowledge major changes between the ancient world as they see it, and our existing one.
How do you think environmental conditions in the deep oceans have changed?
These major changes involved the catastrophic extinction of dinosaurs and countless other animals and species including a great many sea creatures.
It's not quite what you've been led to believe.
Phytoplankton-dependent benthic foraminifera on the deep-sea floor, however, did not suffer significant extinction, suggesting that export productivity persisted at a level sufficient to support their populations. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3271934/
These facts alone at the very least completely changed the environment Coelacanths lived in.
As you now see, the depths of the oceans didn't have that kind of extinction event, except where acidification was an issue. However, it could be the reason that modern coelacanths are different than ancient ones.
Do you deny these claims of major changes by evolutionists
See above. You've been misled about what they say.
No one has told this allegedly 350-million-year-old fish that it was supposed to have been extinct for 65 or 70 million years
Actually, neither of the modern species of coelacanth existed back then. They are of a modern genus unknown in the fossil record. They are still coelacanths, but considerably different than any ancient ones.
Even according to your faulty understanding, this means the fish were not extinct but simply continued to change.
Not very much. But then, they were in an environment that didn't change very much.
Or, how do you know fossils of these coelacanths just haven't been found yet?
Seems unlikely. Even in a constant environment, some changes should occur from neutral mutations.
The following is of some significance as well.https://creation.com/correcting-the-headline-coelacanth-yes-ancient-no
For example, evolutionists once said that amphibians evolved from a Rhipidistian fish, something like the coelacanth. It was explained that they used their fleshy, lobed fins for walking on the sea-floor before emerging on the land.
No. Coelacanths are related closely to the fish that gave rise to tetrapods, but there is no evidence that coelacanths ever used fins to walk. They use them to swim.
As long as the coelacanth was ‘extinct’,
There is no such species as "the coelacanth." It's a very large group, comprised of many species, only two of which seem to have survived. Almost every species of coelacanth is now extinct.
But with the discovery of a living coelacanth in 1938 and their subsequent observation, it was found that the fins were not used for walking but for deft maneuvering when swimming.
Scientists knew this long before living coelacanths were found. Closely related fish, with functional legs, existed long before the modern species. As you just learned, it wasn't coelacanths, but a related group that adapted to walking on the bottom of ponds.
Thus the finding of live coelacanths proved fatal to the idea that such were a ‘transitional form’ from which amphibians (and subsequently land animals and birds) are descended.
And now you know better. Your source had no more idea of how it worked than you do.