This turned out to be a rather long post, so I apologize if it is more information than you wanted. I can only blame you for this post because you asked such wonderful and insightful questions.
I would agree that creationism is primarily a form of denialism.
What I do find interesting within creationist arguments is the appearance that they think fossils are the only evidence we have. Drawing an analogy to criminal law, it is a bit like saying that eyewitness accounts are the only type of evidence we can ever collect. Do we have to have an eyewitness to a murder in order to convict? Do we have to have security camera footage? Or, can we also have forensic evidence such as fingerprints, DNA, fibers, and shoe prints? The same applies to evolution. The most impressive evidence is DNA evidence. We know that species shared a common ancestor because that is what the DNA evidence tells us. We don't need a single fossil in order to determine that evolution is true. Fossils are just icing on the cake.
All species are evolving. As long as you have organisms that produce imperfect copies of themselves (i.e. biological reproduction) and compete for limited resources you will have evolution. Evolution has to happen when these conditions are met because there will have to be winners and losers that are ultimately determined by the DNA sequences they carry in their genomes.
However, not all lineages will see the same amount of morphological (i.e. shape of the organism) change. If selection pressures favor current morphologies then those morphologies will be selected for. Does this mean that there are species that are experiencing no change at all? I highly, highly doubt it because no species is perfect and no environment is perfectly stable. At the DNA level, DNA sequences not under selection will continue to accumulate mutations at a rate consistent with chance, what geneticists call genetic drift.
On top of all of that, we must also remember that there is no objective and non-arbitrary line between one species and the next as we move through time. To use an analogy, it is a bit like trying to pick the nanosecond when you went from being short to being tall. Any point you pick is going to be arbitrary. The way in which we group modern species and fossil species is also arbitrary. We could put all primates in one genus, if we wanted to.
You can't use fossils in that way. Fossils can't tell us who their ancestors were or who their descendants are. It is a misconception that fossils can tell us this. We can use fossils to model what we think a common ancestor probably looked like, but we can never say that any fossil has any descendants.
Fossils are used in a different manner than what you describe. The ultimate test for the theory of evolution is the nested hierarchy, which is analogous to a branching tree. The theory predicts which combinations of features past species should have had, and which combinations species should not have had. For example, the theory predicts that there should have been species that had a mixture of mammal and reptile features, and it also predicts that we should NOT have seen species with a mixture of mammal and bird features. Each and every fossil is a test of these predictions. As of now, every single fossil we have found fits the predictions made by the theory. We only see the mixtures of features that the theory predicts we should see, and we don't see any of the mixtures of features that the theory predicts we shouldn't see.
So to get to your question, the fact that every single fossil we have fits the predictions of the theory of evolution is what tells us that the theory is (tentatively) true. Creationism, on the other hand, makes no predictions about what types of fossils we should find. That is why the theory of evolution is preferred over creationism in scientific circles.
Our common ancestor shared with chimps was a primate. Humans are still primates. Does that not count?
Our common ancestor shared with polar bears was a mammal. Both humans and polar bears are still mammals.
Our common ancestor shared with trout was a vertebrate. Both humans and trout are still vertebrates.
IT would seem that calling two things by the same name is a poor way of determining if evolution has occurred.