re: “Is it possible to believe in both creationism AND evolution?”
As Heartlander pointed out, definitions are crucial in answering your excellent question.
You must understand that there are two schools of thought on Biblical “creationism” - there is the “young” earth creationists that the earth and universe are only 6000 to 10,000 years old, and that the six days are literal 24 hour periods.
There is another Biblical school of thought where “creationism” means that God brought the universe into existence, brought life into existence - all out of nothing - that the general detail given in Genesis 1 that God specially created all living organisms and the entirety of the universe by His power over long periods of time - not, necessarily 6 literal 24 hour days, but rather “ages” of time.
This “old universe/earth” creationism does not hold to evolution in the sense of “macro-evolution” (the view that organisms evolved from single cell to mollusk, from mollusk to fish, from fish to amphibian, from amphibian to some type of land creature - or more simply, the view that simple organisms evolved into more complex ones). This view does allow for evolution “within a given specie” (i.e. the wide variety of the canine specie, feline, etc.) This group does not believe that the fossil evidence demonstrates macro-evolution, rather only micro-evolution within species.
I think this “old universe” creationist group believes that the universe and the earth could have existed long before man - specifically Adam was specially created by God - that there could have been other living organisms/animals before Adam (not human organisms though).
I’m NOT an expert by any means of either group, although I do hold to the old universe/earth and do not believe in theistic evolution.
As to “naturalistic/Darwinian evolution” - that theory really does not allow for God - in fact, He’s unnecessary. According to the theory, all that is came from nothing, simple evolves into complex, that mutations and successful variations of species account for all living organisms.
If you hold to the Biblical view that God specially created the universe and all living organisms - there really is not much common ground between naturalistic/Darwinian evolution and “theistic evolution” - at least that’s the way it looks to me.
Three geologists stand at the foot of Mt. Rushmore. The first geologist says, "This mountain depicts perfectly the faces of four U.S. Presidents, it must be the work of a master sculptor." The second says, "You are a geologist, you should know that all mountains were created by natural forces, such as volcanoes and plate movements, the details were then sculpted by erosion from water and wind. How could you possibly think this was the work of an intelligent sculptor? Only a person completely ignorant of geophysics could think those faces were designed."
The third geologist says to himself, "I don't want to be seen as ignorant, but the faces in this mountain sure do look like they were designed." So he thinks a moment and says to the second geologist, "Of course you are right, these faces were sculpted by natural forces such as erosion. Only an ignorant person would think they were designed." Then he turns to the first and says, "But what a magnificent result, there obviously must have been a master sculptor standing by and watching."
To clarify here. Under this theory God is not necessary to explain how given life you got more diverse life. How we went from the first cell to all the different organisms we have.
The theory of Evolution says nothing about how that first cell came to be. The science on that is highly speculative, and essentially nobody has any real idea. It does not really seem very feasible given what science has discovered, and mostly those that have pet theories on the issue tend to justify them in terms of it being the least crazy ideas of crazy alternatives.
Naturalism implies more than the scientific theory of Evolution, it is a philosophical view that holds that there is nothing super natural in existence, that only the "natural" exists. Materialism...the concept that there is only matter and energy and such is a form of naturalism. If naturalism is true, then not only must the scientific theory of evolution be true (in an unguided sense)--which I personally find plausible, but also abiogenesis must be true somehow (the start of life, how we got to the first cell or other thing that could replicate itself and start mutating in an unguided process), even though this notion is not plausible under current science on my view.
But the least plausible thing Naturalism needs to be true is an explanation of nature itself. The actual stuff and material in the universe. For centuries the idea was that it simply always existed. However science seems to have blown all that up in a big bang. And even before it did, the notion suffered from logical problems that make it infeasible since it implies an actual infinite chain of events in nature, which is not feasible. The alternate explanations are that nature had a beginning yet no cause, that is that something came from nothing. This I find not feasible. There is some confusion about a counter example where you can get energy from empty space in quatumn fluctiations, and thus people say "hey look, something can come form nothing". But this is just a confusion of terms. Empty space is not nothing. It is something that can produce quantumn fluctuations.
Really Naturalism is a failed philosophy decimated by both reason and science. Evolution by contrast s a plausible scientific theory.