Can your worldview explain these two concepts?

1. Because humans are more than animated matter, they are living souls.

2. They couldn't have, information requires a designer, i.e. God.

How did all the information non-materially stored within DNA originate by "chance" when all observable cases of created information involve an intelligent sender?

By simply being not created it doesn't matter what created information involves. It's pomegranates and kayaks. Just because a kayak floats doesn't mean a pomegranate would make a great cruise ship.

Why is the material universe compelled to follow non-material (not composed of matter or energy) laws (i.e. Laws of Logic such as the Law of Non-Contradiction)?

Bogus straw-man division between material and non-material which by the way are decidedly unscientific terms. The word compel implies something outside making things happen. There is nothing outside. Finally, Laws are explanations for how things work. They don't make things work.

1. Oh yeah it can. An invisible magician made it all.

Wait just kidding. The laws of logic (and laws of physics as well) are human descriptions of nature, not prescriptions of that nature. There is a distiction.

2. How do you measure the amount of "information" in a system? It is subjective, since the term refers to statistical data observed by humans. ACTCTATC has just as much information as GGGGGGTC in a DNA sequence. There is no information problem at all, so your question is irrelevant. Information is not stored non-materially, stupid. It is stored by the materials that indicate what human beings call that material. The human concept of what is present isn't a ghost that sits in the material being surveyed. It is a reaction in the human mind.

First of all, I'd like to point out that ignorance does not justify belief in some random idea that answers all of the questions, or fills in the gaps.

1. Laws are not explanations of *why* things occur. Laws are an explanation of what occurs or what is. (i.e. 1+1=2) Theories explain the *why* part. Much of this relates to theoretical physics in general. A topic I would recommend you ask about in the Physics section..

2. What do you mean by 'information stored non-materially'? Could you explain what that is? This relates to abiogenesis and then the process of evolution.

Yes thank you, it does.

1: It is not "compelled", it just does. If God existed, apparently it wouldn't, as He would be fiddling all the time and breaking those "laws".

2: How did all the information stored in the positions of the grains of sand on a beach get there?

Edit:

"There is no information in grains of sand in a beach"

Exactly my point. There is no "information" in DNA, it' a self-replicating molecule.. it just has a rather complicated way of replicating.

And "it just does" answers the question perfectly adequately.

Why does 1+1=2?

There's still no God. ;)

1 - some things are just brute facts, you can't just keep back channeling for explanations forever, e.g. I could keep asking "why does 1+1=2?" and I'd never get an analytic answer

2 - because there was enough time for chance to take its toll, literally billions of years.

1) it isn't

2) cumulative evolution driven by continual adaption to changing environmental conditions

3) learn some basic science and some basic logic

Only with the creator YHVH

Get a education and all will be revealed, including your false premises.