I call the theory naturalistic for the very reason that it takes the naturalistic view of nature. It isn't redundant,it's true.
The problem here is that the sub-text of "naturalistic" is "without God". That is an atheist sub-text which Christians need to disown. There is nothing inherently godless about a naturalistic view of nature.
No,it cannot be verified. The theory is a narrative of the history of life on earth,which is not something that can be repeated by experiment.
This is a misunderstanding of what the theory of evolution is. (We still see some people who don't understand that evolution is both a fact and a theory which explains that fact.) It is time we also began to distinguish between theory of evolution and history of evolution. The theory of evolution is not the narrative of evolutionary history. It is the explanation of the process of evolution which produced that history. So, in a broad sense evolution is not just two things, but three things: a fact, a process (described in the theory of evolution) and a history (the consequence of the process as described in the theory.)
One can indeed confirm experimentally what the process of evolution is, because the process is repeated and repeatable. One can also predict (or more precisely retrodict) what sort of history that process must have produced and test out that prediction via observation.
Order is that which is arranged by intelligence. Functioning order is purposeful,as with organisms. It is not just patterns and sequences that passively occur.
Patterns and sequences are ordered. I don't understand your point.
Natural selection is just the dying off of creatures with certain traits that are thought to be unfavorable to survival and reproductive success,leaving creatures with traits that are thought to be favorable.
Basically you are saying natural selection doesn't do anything important. But it does. New variation can arise through the constant changes that crop up in alleles generated through mutation and recombination. But only selection can favor one variant over another and so create species change (evolution).
It is a process of elimination. Darwin thought that it produced the existing variety of species,but it does not produce anything. Creatures that are better suited to their environment can continue to reproduce without the less suited dying off.
Absolutely. That is why it is not correct to depict natural selection as eliminating only the unfit. It does do that, of course, but it also eliminates the fit when the fitter appear. If the average surviving litter of a species is 10 and the average surviving litter of a new variant is 11, then the day will come when all individuals (or at least all but a very few) in the species express the new variation. That doesn't mean the unchanged individuals were any less fit than their parents or even that their rate of mortality increased.
Theistic evolution is usually just an acceptance of the theory of evolution as it is commonly taught with the claim that God moves the processes of evolution. But the theory itself does not allow for God to be doing anything because it is naturalistic.
Here again we see the sub-text that pits "natural" against God and sees nature as devoid of God unless God intervenes with a non-natural miracle. In the grand tradition of Christian theology it is ridiculous to say that a naturalistic process does not allow for God to be doing anything. That naturalistic process is itself what God is doing. That is why we have summer and winter, seedtime and harvest in due order. That is why we have seeds turning into plants and eggs turning into butterflies or baby chicks. Just because we now have scientific (naturalistic) descriptions of these processes doesn't mean we can send God packing and say "sorry we have automated nature and don't need your help anymore."
And it ignores the fact that species exist as individual creatures (individual creations) that come into being immediately through the means of conception or reproduction
No, it doesn't, That view of the origin of individual creatures is entirely consistent with evolutionary changes in species. Indeed, the theory of evolution insists on the individuality of creatures and there is no reason a Christian cannot understand each conception as a special creation. Species change only because individuals differ from each other and those differences are differently impacted by the world they live in.
(Typically, I find anti-evolutionists speaking as if a species is not a unit decomposable into individuals and speaking of species change as something that must happen to a whole species as a unit all at once. That is an incorrect view of the reality of nature.)
...and instead views species as developing gradually into existence from and into other species,without any specific beginnings.
Generally speaking new species do develop gradually, because a few individual differences are not sufficient to exclude an individual from the species it is born into. No child is a different species than its parent even if it displays some distinct new variation. No new variant in a species is immediately barred from procreation with its fellow members of the same species. In fact, the gradualness of species differentiation is a direct consequence of the fact that species change depends on differences in individuals spreading gradually and preferentially through a species over generations. Individuals have distinct starting points in conception and birth. New species don't.