For Christians (or anyone else) who deny Darwinian evolution.

[I_am_not_mafia]

Being precise and defining our terms is an extremely important part of any dialog. 

True and it's good to see a theist actually try defining precise terms rather than rely upon equivocation. But you are also using the age old theist trick of framing the debate to try and limit the options when it is not warranted. I refuse to keep to your arbitrary limitations. The theory of evolution accounts for all three of the aspects that you describe. They are not three different definitions of evolution, just three aspects that you describe wrongly as definitions. And be aware that it's not a hypothesis, it's a theory. That means that it came about to explain the evidence. The evidence came first. The theory has been tested repeatedly and used in practice.

A simple thought experiment. If Andy believes that our current dog breeds evolved from domesticated wolf ancestors, does Andy believe in evolution? I think it is clear he does. 

If Andy believes in something evolving then how could Andy not also believe in evolution? This is a pointless thought experiment. It's a tautology. If true then true.

But, does he believe that simplicity begat complexity through natural selection acting on random mutations? Does he believe in common ancestry of all living things? We don't know.

The answer to that is whether Andy actually understands evolution. But as Cod says, who the hell is Andy? Why should it matter what one person understands and believes. What matters is what is understood in the scientific literature. This is again the theist trick of trying to frame the debate and to limit the range of answers.

So, it is very obvious that belief of one aspect of evolution does not entail belief in all of them. 

So? The theory of evolution is not a belief. It is an explanation for the evidence. The truth of a description of reality does not depend on who believes in that description. What matters is whether the explanation matches the evidence, whether it is falsifable, reproducible and can be tested. Reality does not change depending on how much people understand.

Regarding your last paragraph, tell me, is the science settled on the following?

a. How complex organs/traits evolved without any survival benefit until they were complete (please give examples of partially formed non-functioning abilities found in nature today)

Irreducible complexity is flawed. It is understood quite well how complexity develops over time. You are the one claiming that complex organs and traits evolved without any survival benefit until they were complete. No evolutionary scientist claims that, only creationists making strawman debates.

b. How are biological networks to have evolved? 

Yes.

c. Why doesn't DNA support the "tree of life"?

Who says it doesn't? Again this is only what creationists claim. I don't even know what this statement could possibly mean.

d. Why there is a glaring lack of fossil records/intermediate forms.  

Again only creationists claim that there is a glaring lack of fossil records / intermediate forms and they will always claim that no matter how many are found. Very few fossils are made. If we find a missing link then this creates two other missing links that they can claim are a glaring lack. We have plenty of evidence from the fossil records.

e. Junk (non-coding) DNA, originally thought of as the leftovers of mutations/transcription errors, yet we continue to discover purposes for it. 

Junk DNA does not disprove the theory of evolution. The neutral gene theory explains that actually junk DNA opens up new areas of search space and can allow for complexity to develop over time. Also see point f.

f. Why natural selection is not enough for traits with a low selection coefficient...yet we have them.

Because there is no benefit in getting rid of those traits and no cost to keeping them so they hang around, like with junk DNA.

I realize there is a theory for every one of these items. My point is, they are not settled, we have no examples, and certainly cannot replicate them in a lab. They remain best guesses. 

Utter bollocks. Again this is you as a religionist claiming this but with no reason to do so. If there is a theory for everyone of these points as you say, then by the scientific definition of theory there is evidence for it. A scientific theory is not a best guess. You do not understand the scientific method, or evolution.

So, if you wish to believe in all three definitions of evolution, it is because you believe in naturalism not because the science is compelling.

No, I believe in the scientific method. I am also familiar with the evidence for the theory of evolution, which includes all three of your definitions (which aren't scientific definitions).